I'm not sure, but it looks somewhat like poison ivy to me. But I haven't had to deal with it for years so may not remember it clearly. At least this answer will take your post back up to the top where people from the Houston area will see it and respond.

I think it is Ampelopsis arborea. It is a very invasive plant. If you don't want it, I suggest you cut the "poppers" and spray them Round up.

Omar

Well thank goodness. Even though Ampelopsis arborea is invasive under ideal conditions, it's much better than trying to protect your self against an allergic reaction to poison ivy.

Omar, isn't that the plant you have growing on the front of your house and passed along to me? If so it can be used as an ornamental vine. The one you gave me is a pretty little thing that has never taken off, probably because if doesn't get enough sun and is planted in unimproved soil.

nrho55, rather than spraying, which can land on good plants, your skin, and inhaled, I drip wide leaf weed killer on the cut stem of unwanted plants to kill them. I wear gloves and am very careful not to get it on my skin.

When dealing with so many plants you might want to get something like the yellow container that "I can't believe it's not butter" comes in. Mark the label well with a lot of big black Xs so it's not ever mistaken for food. You can control the spray top so it barely drips. It's a lot of work initially, but you can get rid of unwanted vines that way. Good luck!

Well, the real 'ratting' is that I thought of that possibly being it, but was too lazy to go out and look at mine for an ID ... :-/

I would have looked up pictures online, but lost it's name when my computer crashed a few months ago. Now I have the name. Thank you .... :P ... *-*

Thank you both so much! It does have about 5 leaves per stem so at this point I'm pretty certain it's pepper vine like you suggested.

It does provide a nice green privacy fence between us and the neighbors but it's absolutely all over, in, and through the grapevines on the same fence. I think I'll have to sacrifice the cover in order to keep the grapes going.

Appreciate the help!
Nadia