Chase is a biter. It doesn't matter where, shoulders, legs, stomach, lips. Just as long as he could sink his teeth in, he didn't care.
During their little tryst, Cameron thought it was just part of his oral fixation. She had limited the amount of kissing, it was too personal, too much of a connection for "no strings attached sex". So she allowed him to amuse his mouth elsewhere.
Annette had believed it was his way of expression during sex. He had never been very happy with his part of the masochist in their games, and the biting was just his way of rebelling against the restraints. She didn't mind, as long as it didn't interfere with her play.
House says that it's a form of vampirism. Come on! The pale skin, piercing eyes, the withdrawn and defensive attitudes towards others. Add that to the biting and the puzzle is solved! Of course that's just what he says. God only knows what he actually thinks, but whatever it is, it's not the truth. If House had figured out the truth, he would have stopped the affair at the beginning.
Chase knows why he bites. He's been taught a hard lesson: nothing is permanent in life and all happiness is passing. When he bites, he creates a new happy memory, to tide him over until the next time an opportunity presents. He bites hard and fast, an attempt to capture the pleasure, or at least make it stay longer. He bites to make an impact, to mark his partners as they leave impressions on him. But in the end, he always knows when to let go. His contentment is not worth the pain he causes others, as he drags them down into his world where happiness is fleeting and the weight of reality crushes all hopes and dreams.