Chloe Dickinson was born 30 Jan 1750, perhaps in Dutchess or Westchester County, New York. A transcription of the family Bible of her granddaughter, Elizabeth Sarah (Wallace) Minard's husband, Isaac T. Minard, gives this birthdate, and indicates that she married John Wallace "of Salem, Dutchess County, New York" and that she was of "his native village."
The problem is that we find no Salem in Dutchess County. There is a North Salem in nearby Westchester County which is where John Wallace's father is buried.
The bigger problem is that we have no clear indication of Chloe Dickinson's parents.
One perplexing clue comes from an 1849 letter written by James S. Wallace, Chloe's grandson. In it, he referring to influence he has with members of the United States Senate, when he says, "As to my own influence in the Senate, Mr. Chase of Ohio is my cousin, Dickinson of NY my father's cousin and Seward an old and attached family friend who when Governor gave my brother in law the second best office in his gift and wrote to me, regretting that I was not in the state to be the recipient of the farms."
We now know that Salmon Portland Chase was indeed James' first cousin by marriage for Chase's wife was Catherine Jane Garniss, James' Aunt Amelia's daughter. We also know that NY Gov Seward appointed Isaac Minard as a judge, and Isaac was the husband of Elizabeth Sarah Wallace, James' sister.
Thus, James was accurate in his depiction of his relationship to Chase and Minard, so it seems reasonable that he would also be accurate in the relationship between his father and Senator Daniel Stevens Dickinson of NY. James specifically indicates that Dickinson was his father's cousin.
James Dickinson Wallace, James S. Wallace's father, was the son of Chloe Dickinson Wallace. Since the letter indicates that Senator Dickinson was a cousin of James Dickinson Wallace, it follows that, to be a first cousin, the Senator would have to be a child of a sibling of Chloe Dickinson Wallace.
Alas, it does not appear to be so.
Senator Daniel Stevens Dickinson's parents were Daniel Thomas and Mary (Caulkins) Dickinson. In chapter 20, Town of Guilford, taken from History of Chenango and Madison Counties by James H. Smith, written in 1880, and transcribed at the link above, we find the following information:
"Settlements were made in 1807 by Daniel Thomas Dickinson and Samuel Mills, both of whom came from Connecticut, the former from Goshen and the latter from Norfolk. Dickinson settled one and one-half miles north of Guilford Center, on fifty acres, to which he subsequently added at different times 200 acres. ... The Dickinson family is a prominent and highly reputable one and has been made conspicuous by at least one of its members both in the State and nation. Mr. Dickinson married Mary, daughter of Roswell Caulkins, of Salem, Conn., and sister of Hon. Samuel A. Smith's mother. He continued to reside here till his death Sept. 17, 1841, aged 74, and raised a family of sturdy, stalwart children---stalwart both intellectually and physically. His wife died April 1, 1831, aged 61. His children were Erastus, William Frederick, Ann Pomona, who married Alpheus Johnson, and is now living in Afton, aged 81 years, Daniel Stevens, Thomas, Ralph, who died in Goshen at the age of four years, John Ralph, and Mary Sophronia, who died at the age of five years."
That gives us Daniel Thomas Dickinson's dates: born about 1767, died 17 Sep 1841.
From the Minard family Bible, we know that Chloe was born 30 Jan 1750 and died 28 Feb 1815.
If Daniel Thomas and Chloe were siblings, then she would have been one of the first born, and he one of the last, but it is still possible to hold them brother and sister.
However, according to "To the Descendants of Thomas Dickinson, Son of Nathaniel and Anna Gull Dickinson of Wethersfield, Connecticut and Hadley, Massachusetts," compiled in 1897 by Frederick Dickinson of Chicago, Daniel Thomas Dickinson was a son of Thomas and Mary (Stevens) Dickinson who married 25 Jun 1760, and Chloe does not appear as a child of this couple. This book is available online here.
According to this book, Thomas Dickinson, who married Mary Stevens, was a son of Thomas and Ann (surname unknown) Dickinson. This Thomas, wife of Ann, is said to have been born in 1708 and died in 1747. Ann Dickinson was born 15 May 1715 and died 29 Nov 1796. She would have been 35 in 1750.
The name Chloe does not appear in this book.
So, thus far we have no evidence that Chloe was a daughter of either Daniel Thomas Dickinson or his father Thomas Dickinson. The first would make her a first cousin to Daniel Stevens Dickinson, the latter a second cousin.
So we are back to square one. Who were Chloe's parents? Do you know?