I used to have a coworker like that but the good thing is, she is aware of her problem and let me in on it. She had told me she was jealous because our boss lend me a job-related book to read first. There is only one copy and we have to take turn. I ended up giving it to her so she gets to read it first. She told me it is in her nature to get jealous easily and she does not know why.
I actually feel sorry for such people and if I am comfortable enough, I try to "help" them out and suggest some kind of counselling. No one is perfert. All of us have some sort of shortcoming and I don't want to be too harsh on anyone.