Being Naturalized in 1843 means he was still a British Citizen when Chester was born (1829). That means....even if Chester was born on our soil (some say Canada) he still had dual citizenship by descent from his father. Thus, according to the Constitution he was not naturally born a citizen but acquired it when his father naturalized.
He kept this information private when he ran for vice president in 1880 with Garfield heading the ticket.
The Constitutional requirements to be Vice President are identical to those needed to be President.
Herbert Hoover’s Vice President, Charles Curtis wasn’t born in a state of the Union (Kansas Territory a year before statehood) and he was an enrolled member of a sovereign Indian Nation (The Kaw Nation) making him also a dual citizen.