While military obligations complicated Chistov's transfer to North America, he and fellow draftee Alexander Frolov left Russia anyway, in 2002, ultimately signing with the Ducks after a prolonged dispute with Russian officials.

The next year, Chistov struggled, and he was sent down to Anaheim's American Hockey League (AHL) affiliate, the Cincinnati Mighty Ducks.

He remained there during the 2004–05 NHL lockout, until he decided he did not want to play in the minor pros, and he and the club parted ways.

Chistov returned to Russia for the 2005–06 season, where he enjoyed a solid campaign playing on Evgeni Malkin's line for the Super League's Metallurg Magnitogorsk.

In the summer of 2007, Chistov signed with Salavat Yulaev Ufa of the Russian Super League.