As theFeeble said, made popular by 'pop-punk' bands Green Day and Offspring (I no longer class Offspring as punk - they had their time before they sold out).
However the wallet chain was originally used by skateboarders to keep their wallets after they had fallen over. Afterwards they became something of a fashion statement to say that 'I listen to skate punk music.' Now overpopularised by people that think it's trendy (which it unfortunately is).
Nowadays not always accompanied by a wallet, and also may be worn by a member of a boy band like N*Sync or A1 (as I recently witnessed on TV).