Is it better to ask her if she loves you even though you know there is no chance?
How do you know you don't stand a chance? Of course ask her. The worst is a "no" and we can all get that several times in our lives. Don't go through life regretting you never asked. Don't have a long life of "what ifs." Good luck!
It's really up to you. Ask yourself how you will handle it if she says she has no interest in you. If you really aren't ready for "no" as an answer yet, then you might want to try being friends with her and seeing what might develop. On the other hand, if your feelings are overwhelming you so much that it's causing you to put your life on hold, I would recommend that you tell her about your feelings and ask her about hers.
I've always been the type to take the risk because I couldn't stand the thought of "what might have been" if I hadn't. Good luck, and trust that if she doesn't share your feelings, someone will come along who will.