Arthur was born in Vermont.
However, his father was a Canadian (or Irish?) citizen when Arthur was born. He has not yet become a US citizen.
Census records seem to prove this and fwiw. His father,William Arthur was born in British Northern Ireland. He was an immigrant to Canada. He settled in Dunham, Quebec which is near to Fairfield, Vermont. He married a Fairfield lady and the census tells us much.
The daughter was born in Canada and the baptismal register for her proves that. The census dutifully records her birth in Canada. Chester Arthur is twice recorded on two successive census as being born in Fairfield, Vermont. A certificate of citizenship shows William sworn as such in 1843, when Chester is 14 years old.
Even then when Arthur took the place of the murdered president, there was a flurry of questions regarding eligibility. A lawyer called Hinman (Democrat)wrote a book titled "A British Subject is in the White House".
The Republican Party turned down the offer to stand for president by Chester Arthur. Some say it was because of the eligibility clause. Almost unheard of to refuse an standing president. Their chosen man lost to the Democrats.
Bit of a ramble and please excuse me for it.