The Liars' Club

A valuable painting was stolen from the Liars' Club, but the police are having a hard time identifying the culprit because every statement made by members of the Liars' Club is false. Only four members visited the club on the day that the painting was stolen. No two members were ever present at the same time. This is what they told the police:

• Ann: "None of us took the painting. The painting was here when I left."
• Bob: "I arrived second. The painting was already gone."
• Chuck: "I was the third to arrive. The painting was here when I arrived."
• Tom: "Whoever stole it didn't arrive after me. The painting was already gone."

Who stole the painting?