The state of being completely oblivious to a girl's chest. This could be due to her perfect ass, legs, face, personality (yeah right), alcohol, video games, etc.
This is not to be confused with being gay or polite. The word in question refers to completely not noticing a beautiful pair of jugs, not intentionally disregarding them.
"I had such a legitimate crush on Jody that I didn't realize for a full month after I met her that she had the most amazing rack in the entire school. I was titblivious around her."
Girl 1: "Hey! Does this shirt make my boobs look awesome?"
Guy: "Yeah whatever. TOUCHDOWN!"
Girl 2: "Don't mind him, he's titblivious when football's on."