Am I allowed to bring glass items on a carry-on on a plane?

I have a set of shot-glasses which I bought as a gift and I want to bring them back home. I don't want to put them in my checked luggage because I am afraid that they will break plus I don't have anymore space in my suitcase. Am I allowed to bring them with me on the plane? I didn't find them in the prohibited items list of the TSA (Transportation Security Administration). Did anyone have a problem with a glass item at a checkpoint?