If it's a literal burn, douse it thoroughly with cool water and get to an urgent care. If it's a burning sensation, take some tums and an aspirin and try burping a lot. You may also want to thoroughly apply some Icy-Hot. A cool bath couldn't hurt.
If it lasts longer than a couple of hours, get to a hospital ASAP and have your heart checked.
Source: My uncle's a medical professional. That makes me a slightly more reliable source than the average person.