Looks like they are already releasing one of their 4 campaign DLC's - next tuesday! This one is called 'Captain Scarlett and Her Pirate's Booty' and is not free
Don't know about you, but this seems a tad early to be releasing a campaign DLC, considering the game has not been out for very long. Anyway, check this link
for details. It apparently costs $9.99. Hmmmm.