It has been suggested that Palmer was born in Yetminster, England, in 1585. He married in England and fathered five children, but it is not known who his first wife was. It is said that on April 5, 1629, he sailed on the Four Sisters from Gravesend, England, to Salem, Massachusetts, arriving that June. The next year, Palmer was indicted on manslaughter charges for allegedly beating a man to death. He was acquitted in November 1630. His close friend, William Chesebrough, stood as one of the witnesses in the trial.
Palmer and Chesebrough took the Oath of a Freeman on May 18, 1631. In 1633, Palmer married a second time, to Rebecca Short. They eventually had seven children together. In 1635 Palmer was elected a selectman of Charlestown and the next year became constable.
On August 24, 1643, Palmer and Chesebrough left Charlestown and started a new settlement called Seacuncke (later renamed Rehoboth). Palmer was among the first selectmen. When the settlement assigned itself to Plymouth Colony, the deputy elected to represent Rehoboth at the Plymouth court refused to serve because he preferred attachment to the Massachusetts Bay Colony. Palmer was then appointed in his place.
Palmer and Chesebrough were also dissatisfied with the Plymouth alignment, and sometime prior to 1653 John Winthrop, Jr. persuaded Chesebrough to relocate to southern Connecticut. Chesebrough obtained a land grant in present-day New London, Connecticut; Palmer and his son-in-law Thomas Miner followed him and purchased land on the east bank of Wequetequoc Cove, across from Chesebrough, in present-day Mystic, Connecticut.
In August 1652, Miner built his father-in-law and himself a house on their land; the next year, both their families joined them, and other settlers soon followed. The group struggled for years for self rule. During that time, Palmer served as constable and again as a selectman. It took until 1661 to build a church meetinghouse due to resistance from the General Court of Connecticut, which preferred the colonists travel across the river to New London. Palmer died two months after the meetinghouse was first used.
The 300-year Stonington Chronology describes Palmer as the
"...patriarch of the early Stonington settlers...(who) had been prominent in the establishment of Boston, Charlestown and Rehoboth, ...a vigorous giant, 6 feet 5 inches tall. When he settled at Southertown (Stonington) he was sixty-eight years old, older than most of the other settlers.