Don't hold your breath, man. Your best bet is to farm named mobs, as most of them have a specific legendary tied to them with a higher drop percentage. Rates seem to vary from ~1% to ~5%. Getting a legendary from a chest is probably in the fraction of a percent range.
I've gotten two so far. A Royal Deliverance shotgun and a Baby Maker SMG. The SMG was a random drop on PT1 with a friend, I forget where the RD came from.
Lol, Cardboard and I ran through the Warrior today, first time playing against him I didn't even get a purple drop, three minutes later I shot a slagged psycho in eridium blight and it dropped the Flakker shotgun.