Bob, have you tried any other appliances in that outlet? And, was the other outlet you tried on the same circuit? I would try to make sure it's not the GFCI outlet (they can go bad), or the circuit breaker in your panel.
If you're sure your wiring is OK, then I'd recommend taking the back off the smoker and checking the wiring. Make sure all connections are tight, and none of the wire is under the last layer of insulation (against the inside back wall of the smoker). It may be that you have a loose connection that is either causing a short, or is getting hot enough to trip the GFCI plug.
Maybe some of our electrical experts will sound off, too!