At a distance the vine appears to be Virginia Creeper, a very aggressive vine(and on the invasive list in some states. I really can't help with how to get rid of it. Other than move! lol I only battled it once at my old home (no I didn't move to get rid of it)and never succeeded in overcoming it's hold on my front porch post.
To help you, I searched the net for a way to get rid of it and, to be honest, didn't find anything except for people saying how impossible it is to get rid of. A DG member wrote that she was having some luck covering it with black plastic and covering with newspaper, leaves. Not sure if this is feasible on a climbing Virginia Creeper. I think her's was a groundcover situation.
I totally agree after seeing a close up shot of the leaves. Not Virginia Creeper. Rusty you might try posting your close-up pic in the Plant ID and Invasives forums. Good luck. It does look like you need to do something asap as it has grown alot in a few days.
I am fairly certain that it is "winter creeper" also known as "climbing euonymus" or "euonymus fortunei" (Celastrales: Celastraceae) It is native to Asia and has become quite invasive in my area (Southeast.) Still, some of my neighbors continue to encourage it...
Rusty56, I think I have this vine on my hickory tree too, are the leaves thick and fleshy and shinny? The only way I've been told here in the country is to cut the vines where they start up the tree, it works for a while but you have to keep doing it, I have two stumps about 15' apart in my back yard that have this vine all over it and I have sprayed with weed killer it turns it brown for a while and then it greens up again, I've been told to put 1/2 fuel oil and 1/2 gas on it but just can't bring myself to do that to the ground around it, the ivy is going away from the stump onto the ground about 3' around it searching for something else to crawl up! It has a very woody stem. I have seen big tall oak trees brought down by this vine it sucks the life right out of them! That sure looks like that vine I have from your picture.
I looked up what keelmt has suggested "climbing euonymus", and it says not to cut down at the root that it will only make a better root system here is the link and it says to cut and spray with roundup and water the roundup into the roots at 40 degrees, that temp. should be easy for here right now if we could find a dry day it's been raining for three days and have about three days to go yet :)
Here is the link it shows orange berries like I have on mine right now: