An article of clothing, usually a shirt, that one gets for free. The most likely source is a contest at a bar/club or a freebie from a liqueur distributor. Hence the Zero Dollar Status. It can be an insult given to someone that should know better than to wear it out on the town.
Steve: Yo' Charlie! Can you believe Willy is wearing that Zero Dollar shirt he got from Miller? I’m surprised the bouncer let him in!
Charlie: Fo shizzle my nizzle, why do you think he wins the Golden Corona every Year?