Whether he was born in Canada or Vermont, the controversy over Chester Arthur’s NBC status birth should instead center around his father’s citizenship which I believe was not granted until 1843, fifteen years after his son Arthur’s birth in 1829.
That is one murky nest of weeds.
While Chester’s father, Reverend William Arthur, was foreign born, he had immigrated to the United States from northern Ireland when he was 18 and had become a Baptist minister. Chester’s mother, Malvina Stone Arthur, was born in New Hampshire. The Arthurs had four daughters when Chester was born. When the family was complete, Chester had a brother and another sister.
I did not find any material on when/if Rev William Arthur became an American citizen. By 1822 the family had settled in Vermont, his parents having met in Quebec. Chester was born in 1829. The “born in Canada” rumor spread by an enemy, Arthur P. Hinman, was debunked. Arthur P. Hinman actually spread two sets of rumors, one that Arthur was born in Ireland & emigrated to the US at age 14, the second the rumor that Arthur was born in Quebec. Both allegations were resoundingly disproven. I do not see that his father’s citizenship was raised as an issue. It certainly would have been if it could have aided Chester’s enemy’s claims.
In the early 1800’s a potential citizen could go to any court of record after two years residency in the U.S. and file a declaration of intent to become a citizen. Then after three more years the immigrant could seek naturalization papers to complete the process. There was certainly enough time for that process before Chester’s birth.