Sandman87 . . . I think the repaired antler is from Dr. Hiruluk, Chopper's mentor. The man-reindeer befriended the noted quack of Drum Island, and apprenticed under him. When Dr. H got sick, Chopper searched for a rare ingredient for a supposed remedy. Along the way, he ran afoul of some reindeer (I think), and his antler got snapped as a result. At least that's how I remember the antler getting fixed. He might not be able to shed the antlers after eating the Human-Human Fruit (no, really), since they get sucked into his head when he grows into his "monster" mode.
Chopper's backstory is pretty tragic. Before eating the Devil Fruit, he was ostracized by other reindeer for his blue nose. Also, the "remedy" I mentioned before was actually a poison, and Chopper had thought the skull and crossbones was a good sign. Dr. Hiruluk actually did want to die, as he suicide-bombed himself to try and show up Drum Island's dictator, the omnivorous Wapol. Once again . . . that's how I remember things, and I could be wrong. Add that to Luffy and Sanji wanting to cook him up when they first met, it's amazing how well-adjusted Chopper is, naivete aside.