Yes, if Birtherism is correct, Arthur was not a "natural born citizen." But he was elected to the Vice-Presidentcy, and served for years as President. So, either:
A. Arthur was ineligible to be elected to either the Vice-Presidentcy, or serve as President, and everybody back in the 19th century was just too stupid to understand that; or,
B. Birtherism is wrong.
Which is more likely?
Apparently you don't know history. This is a link to a legal brief and info on A Hinman, a private investigator, searching for info on Chester Arthur.
New evidence came to light on December 6, 2008 which revealed that the naturalization records for President Chester Arthur's father, William Arthur, had been located in the "Chester A. Arthur Papers" at the Library of Congress. The New York State record proved William Arthur wasn't naturalized as a United States citizen until August 1843, fourteen years after Chester Arthur was born in 1829. The fact of Chester Arthur's having been born a British subject was published for the first time on Dec. 6, 2008 and is therefore an "intervening matter not available at the time of the party's last filing."
The definitive biography of Chester Arthur's life is “Gentleman Boss” by Thomas Reeves. Since Chester Arthur burned his papers around the time of his death, this biography fills many gaps with interviews of family members and authentic documents such as the Arthur family Bible. "Gentleman Boss” establishes, on page 4, that Chester Arthur’s father William was born in Ireland, 1796, and emigrated to Canada in 1818 or 1819.
He also burned his personal papers near the time he died. Chester Arthur's attempt to obfuscate family history during the 1880 campaign provides context that he believed his birth as a British subject made him ineligible to the office of Vice President.
And you obviously didn’t read the link.