No one ever objected to Chester Arthur's eligibility on the grounds that his father wasn't a citizen. Some opponents of his raised the possibility that he was born in Canada, but that's an entirely seperate matter.
In point of fact, in the entire history of the United States, no major party's presidential candidate has ever been challanged on these grounds, despite the fact that multiple candidates were nominated who had at least one non-citizen parent.
During the campaign of 1880, questions were asked about Chester’s birth place, but just as today, those doing the research were looking in the wrong direction. Arthur’s father, William Arthur was a British citizen at the time of the future President’s birth. Born in Ballymena, Ireland in 1796 he would not become a Naturalized citizen until August 31st, 1843. No one ever checked into his immigration status at the time of his son’s birth. Chester Arthur, 14 at the time his father was naturalized, and would surely have known this. Sound somewhat familiar?
No one knew Arthur was not a Natural Born Citizen. No one knew during the campaign or ever until 2008 that William Arthur did not become a Naturalized citizen until his son was 14.
That being said, a number of interviews were published in the Brooklyn Eagle regarding Hinnman, the man principally investigating Arthur. August 1880 is where to start your searching bubba. Clearly August 1880 was before the Nov 1880 elections.
FAIL!