It could mean a lot of things, depending on which part of your chest is hurting, what kind of pain you are having, what other symptoms you are having etc..
Next Steps
If the pain is causing you trouble, it is better to consult your physician in person so that they can examine you and if needed do some tests to find out what is wrong.
Health Tips
Pain with deep breath could be a sign of some lung problem. So if you have associated breathing difficulty, I suggest you consult a doctor soon.