The competition was announced by Hugh Jackman, who plays Wolverine, on YouTube. The competition requires fans to go to a microsite for the film and vote for their town.
The town with the most votes will be announced on April 20. The premiere is set for April 27 with the film set to be released elsewhere in the US on May 1.
However Wolverine fans might not have to wait that long. Shortly after the competition was announced it has been discovered the film was leaked online earlier this week.
According to file sharing sites around 75,000 Wolverine downloads have already been made. Comments from users suggest that although the film is missing some of its special effects it is largely complete.
In a statement Fox said: "We forensically mark our content so we can identify sources that make it available or download it.
The source of the initial leak and any subsequent postings will be prosecuted to the fullest extent of the law. The FBI and the MPAA also are actively investigating this crime."
The film tells Wolverine's story before he met the other characters in the X-Men series.