I think it's an Ampelopsis. Look for Ampelopsis aborea pictures and A. megaphylla to compare.
Where is this growing? What state?

Oh, I believe you hit the nail right on the head! It looks exactly like the photos of the Ampelopsis arborea. Right down to the climbing tendrils and red stem. Also known as peppervine.

It's growing in our back yard in an urban setting in southwest TN.

Thank you, thank you!

Here is a link that might be useful: http://www.sfrc.ufl.edu/4h/Peppervine/peppervi.htm