Coworker Issue...Should I tell the boss?

I had the same problem at work. Don't expect your boss to punish her when the boss goes to your coworker to chat. Nicely speak with your boss and explain your feelings to her. Some bosses don't have backbone so she may not have the confidence to do anything about your concern. It is healthy for you, however, to let your boss know. I did and my boss stated that he sees the work I do. Situations were better after talking to him. Good luck.