My chicken is having trouble laying her egg?

I agree, it sounds like a case of egg-binding, and your hen will almost certainly die if you don't get her to a vet ASAP. There isn't too much you can do with a situation like that at home, except make sure she at least has access to water and a bit of food and is in a warm, dry spot until you can take her to the vet. If you need more information before doing that, I recommend asking on Backyard Chickens forum. It could be something else is wrong with her, but the situation sounds pretty bad, so the best thing to do would be to take her for a vet visit.