She is engaged. End of story.
Your chances are most likely zero for the above reason. Please don't waste your time thinking (hoping) that she will have a falling out with her fiance and suddenly become available again. I have done this before, and it is a sure fire way to get yourself really hurt, especially when you have to deal with them talking about their upcoming wedding, etc. etc. It is especially bad if it is a coworker that you have to see all the time and they are kind of in your face about it.
Do yourself a favor, treat the chick like she is already married and forget about her, and look for a (really) single woman. It will save your sanity in the end and keep you from getting burned badly!