In the 2 minutes that I spent googling the topic, the majority of the information I received stated that Tennessee honors North Carolina's CHP. Obviously there are going to be differences in state laws, and you'll have to abide by TN's laws while in their state, regardless of where your permit is from.
Don't take my word for it, though. I strongly suggest you find a trustworthy source to verify that for yourself. I hope that helps!