Thanks for your reply and see this post:
http://www.freerepublic.com/focus/news/3382753/posts?page=447
And see also that Chester Arthur’s father was an immigrant and didn’t become a citizen before his birth:
“Arthur was born in Vermont to a Vermont-born mother and a father from Ireland, who was naturalized as a U.S. citizen in 1843, 14 years after Chester was born. Despite the fact that his parents took up residence in the United States somewhere between 1822 and 1824, Arthur additionally began to claim between 1870 and 1880[82] that he had been born in 1830, rather than in 1829, which only caused minor confusion and was even used in several publications.[83]”
https://en.wikipedia.org/wiki/Natural-born-citizen_clause#Chester_A._Arthur