Insolence

What is the best way to deal with a rare but habitual string of petty, passive aggressive insults from one of my employees? I'm a strong proponent of a fun workplace environment and team camaraderie, and, while her behavior unarguably works against both, I fear that confronting her about something relatively minor is likewise counter-productive. She is by far the hardest worker on my staff, and the box office would not be running nearly as well without her. I praise her for this often. Nevertheless, there still seems to be a chip on her shoulder when it comes to authority (regarding both me and much moreso with my boss); everyone is a clueless loafer except for her.

I also am trying to make sure that I approach this from a professional, administrative perspective, despite my natural inclinations to take things personally. If it does become necessary to address the issue with her, I will need to take extra precautions to ensure that our conversation remains official/detached.