Chester A. Arthur destroyed all the evidence before he died, I don’t think it can be proven one way or the other.
Father William Arthur, was born in Dreen, Ireland.
Naturalized as US Citizen in the Court of Common Pleas, Salem, Washington County, NY on August 31, 1843, (Almost 14 years after the birth of Chester.)
Mother Malvina Stone born in VT
Both parents were not US Citizens at the time of his birth.
Chester A Arthur was NOT a Natural Born Citizen.