Thomas Hazard migrated to New England during the Puritan Great Migration . , by R. C. Anderson, vol. 3, p. 294-8)
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Direct quote from: The Hazard family of Rhode Island 1635-1894 : Being a genealogy and history of the descendants of Thomas Hazard, with sketches of the worthies of this family, and anecdotes illustrative of their traits and also of the times in which they lived. by Caroline E Robinson. Copyright, 1896. page 1-2.

Thomas Hazard, the progenitor of the Hazard family in the United States of America, was born in 1610; he died in 1680; he married, 1st Martha ____, who died in 1669. He married, 2nd, Martha, widow of Thomas Sheriff; she died in 1691.
His name is first found in Boston, Massachusetts, in 1635. In 1638, March 25, he was admitted freeman of Boston. Two years later he was admitted freeman of Portsmouth, Rhode Island. in 1639, April 28, he and eight others signed the following contract, preparatory to the settlement of Newport Rhode Island: “It is agreed by us whose hands are underwritten to propagate a plantation in the midst of the island or elsewhere, and to engage ourselves to bear equal charge, answerable to our strength and estates, in common, and that our determination shall be by major voice of judge and elders, the judge to have a double voice.” The founders and first officers of the town of Newport were William Coddington, Judge; Nicholas Easton, John Coggeshall, William Brenton, John Clarke, Jeremy Clarke, Thomas Hazard, and Henry Bull, Elders; William Dyre, Clerk. In 1639, June 5, he was named one of four proportioners of land in Newport, any three of whom might proportion it; “the company laying it forth to have 4d. an acre for every acre laid.” September 2, 1539, he was admitted freeman of Newport, and in 1640, March12, he was appointed a member of the General Court of Elections. In 1665, he was for a short time in Newtown, Long Island. In his will, proved 1680, his wife Martha, whom he calls his “beloved yoke-fellow,” is sole executrix, and he fives her “all movable and immovable estate, as housing, goods, cattle, and chattels, etc.” To his son Robert he gives 1s. To his daughter, Hannah Wilcox and Martha Potter, wife of Ichabod Potter, 1s. There is a long line of descendants from this daughter Martha, and Ichabod Potter, with frequent intermarriages in the Hazard family. In the early history of the family it was almost an exception to find a Hazard who did not marry a cousin, and it is a curious fact that the lines in which these marriages were the most frequent, were often marked by the strongest men and women, both mentally and physically.
These few meagre facts are about all that can be found at the present day of the founder of the Hazard family in America. But Thomas R Hazard, in his Recollections of Olden Times, has given an account of the family that goes back, even beyond the names; its European founder being the Duke de Charente, living about 1060, on the borders of Switzerland. From the Duke de Charente he has given an interesting account of the changes in the name, until toward the close of the eighteenth century, when it was, and still continues to be written Hazard. Willis R Hazard, a descendant of Johathan Hazard of Newtown, Long Island , has given us the chief characteristics of the family; and although his account was intended for the descendants of Jonathan of Newtown, it is equally applicable to the Rhode Island family. He says: “The Hazards are a strongly marked race, handing sown and retaining certain peculiarities from generation to generation. One is, a peculiar decision of character, a certain amount of pride, and a pronounced independence, coupled with a slight reserve. Physically they are strongly marked. Generally speaking, they are of good stature and vigorous frames with rather a square head, high forehead, brown hair, blue eyes, straight or aquiline nose, and with will shown by a firmly set jaw. Their complexion is fair, a little inclined to florid.”
Few families in Rhode Island have a brighter record than the Hazard family, where, if greatness is not always found, sobriety, honesty and integrity make even the humblest lives worth studying; and when one finds, as is often the case, a retiring, unpretentious modesty combined with greatness, he must be pardoned for his enthusiastic admiration for the old family tree, that still sends out vigorous shoots after more than two hundred years of grown in America.
Children of Thomas Hazard:
2. Robert Hazard, born 1635, in England or Ireland; died 1710; married Mary Bownell
3. Elizabeth Hazard, married George Lewton.
4. Hannah Hazard, married Stephen Wilcox, son of Edward Wilcox.
5. Martha Hazard, married 1st, Ichabod Potter, son of Nathaniel & Dorothy Potter; married 2nd, Benjamin Mowry, son of Roger and Mary Mowry

Direct quote from: The Hazard family of Rhode Island 1635-1894 : Being a genealogy and history of the descendants of Thomas Hazard, with sketches of the worthies of this family, and anecdotes illustrative of their traits and also of the times in which they lived. by Caroline E Robinson. Copyright, 1896. page 1-2.

Thomas Hazard, the progenitor of the Hazard family in the United States of America, was born in 1610; he died in 1680; he married, 1st Martha ____, who died in 1669. He married, 2nd, Martha, widow of Thomas Sheriff; she died in 1691.
His name is first found in Boston, Massachusetts, in 1635. In 1638, March 25, he was admitted freeman of Boston. Two years later he was admitted freeman of Portsmouth, Rhode Island. in 1639, April 28, he and eight others signed the following contract, preparatory to the settlement of Newport Rhode Island: “It is agreed by us whose hands are underwritten to propagate a plantation in the midst of the island or elsewhere, and to engage ourselves to bear equal charge, answerable to our strength and estates, in common, and that our determination shall be by major voice of judge and elders, the judge to have a double voice.” The founders and first officers of the town of Newport were William Coddington, Judge; Nicholas Easton, John Coggeshall, William Brenton, John Clarke, Jeremy Clarke, Thomas Hazard, and Henry Bull, Elders; William Dyre, Clerk. In 1639, June 5, he was named one of four proportioners of land in Newport, any three of whom might proportion it; “the company laying it forth to have 4d. an acre for every acre laid.” September 2, 1539, he was admitted freeman of Newport, and in 1640, March12, he was appointed a member of the General Court of Elections. In 1665, he was for a short time in Newtown, Long Island. In his will, proved 1680, his wife Martha, whom he calls his “beloved yoke-fellow,” is sole executrix, and he fives her “all movable and immovable estate, as housing, goods, cattle, and chattels, etc.” To his son Robert he gives 1s. To his daughter, Hannah Wilcox and Martha Potter, wife of Ichabod Potter, 1s. There is a long line of descendants from this daughter Martha, and Ichabod Potter, with frequent intermarriages in the Hazard family. In the early history of the family it was almost an exception to find a Hazard who did not marry a cousin, and it is a curious fact that the lines in which these marriages were the most frequent, were often marked by the strongest men and women, both mentally and physically.
These few meagre facts are about all that can be found at the present day of the founder of the Hazard family in America. But Thomas R Hazard, in his Recollections of Olden Times, has given an account of the family that goes back, even beyond the names; its European founder being the Duke de Charente, living about 1060, on the borders of Switzerland. From the Duke de Charente he has given an interesting account of the changes in the name, until toward the close of the eighteenth century, when it was, and still continues to be written Hazard. Willis R Hazard, a descendant of Johathan Hazard of Newtown, Long Island , has given us the chief characteristics of the family; and although his account was intended for the descendants of Jonathan of Newtown, it is equally applicable to the Rhode Island family. He says: “The Hazards are a strongly marked race, handing sown and retaining certain peculiarities from generation to generation. One is, a peculiar decision of character, a certain amount of pride, and a pronounced independence, coupled with a slight reserve. Physically they are strongly marked. Generally speaking, they are of good stature and vigorous frames with rather a square head, high forehead, brown hair, blue eyes, straight or aquiline nose, and with will shown by a firmly set jaw. Their complexion is fair, a little inclined to florid.”
Few families in Rhode Island have a brighter record than the Hazard family, where, if greatness is not always found, sobriety, honesty and integrity make even the humblest lives worth studying; and when one finds, as is often the case, a retiring, unpretentious modesty combined with greatness, he must be pardoned for his enthusiastic admiration for the old family tree, that still sends out vigorous shoots after more than two hundred years of grown in America.
Children of Thomas Hazard:
2. Robert Hazard, born 1635, in England or Ireland; died 1710; married Mary Bownell
3. Elizabeth Hazard, married George Lewton.
4. Hannah Hazard, married Stephen Wilcox, son of Edward Wilcox.
5. Martha Hazard, married 1st, Ichabod Potter, son of Nathaniel & Dorothy Potter; married 2nd, Benjamin Mowry, son of Roger and Mary Mowry