There is some confusion over the names of Sarah's parents. Wikitree has her as the daughter of Nathaniel Chesebrough and Hannah (Denison) Saxton, as does findagrave.com. I found an Ancestry.com tree that listed har parents as Samuel Cheseborough and Abigail Ingraham. One family source and Brownings "Americans of Royal Descent also have her father as Samuel, not Nathanial.
Colonial Days and Ways by Helen Evertson Smith states:
"William Gallup, a son of the second John Gallup and Hannah Lake, married Sarah, a daughter of Samuel and granddaughter of William Chesebrough of Stonington, Connecticut." (https://ia800500.us.archive.org/0/items/cu31924028729378/cu31924028729378.pdf)
Browning, pg. 151: "William Gallup, of Stonington, Conn., third son, who married Sarah, daughter of Samuel Cheesbro..." (https://books.google.com/books?id=dIUaAAAAYAAJ&pg=PA151&lpg=PA151&dq=browning+americans+of+royal+descent+gallup&source=bl&ots=0k_XHDo8XD&sig=yQF4qNo91nPiFmQqa8vSc5KFLYg&hl=en&sa=X&ved=0ahUKEwjImpO2lcXZAhVGQ6wKHZC7CD0Q6AEINjAD#v=onepage&q=browning%20americans%20of%20royal%20descent%20gallup&f=false)
"Connecticut marriages 1640-1939" (fasmilysearch.org" cites a Sarah Chesebrough, daughter of Nathaniel, dying in 1707. Sarah, the wife of William Gallup, died in 1729 as per her gravestone, so this likely proves Sarah, the wife of William Gallup, was the daughter of Samuel Chesebrough, not Nathaniel. The Barbour Ct. vital records do show Nathaniel had a daughter Sarah born 1662 and Samuel had a daughter Sarah born 1663.
"History of the town of Stonington" pg. 292 shows her as the daughter of Nathaniel Chesbrough and Hannah Denisnon, while "Genealogical history of the Gallup family (pg. 27) has her as Samuel's daughter.