From your description, I'd guess Virginia creeper, which is also called woodbine. It can be a rampant grower and would probably cover that fence in no time, but I might pass on it. It's in the grape family and has fruits that look a little like wild grapes, but I believe they're poisonous. I once bit one accidentally while picking wild grapes (they were growing intermingled). It was one of the foulest things I've ever tasted. Plus, the vines might soon become heavy enough to knock down the fence--they will take over and cover small trees, given the chance.

Here is a link that might be useful: {{gwi:1053941}}

V.c. is considered poisonous. Wild grape isn't, so that would probably be a reassuring choice for you. It also grows vigorously. If the chain link fence was installed correctly the vine won't pull it down. My neighbor has this setup and the vine is at least a decade old. Most years it also gets some nice fall color as well. It grows wild all over the place, I'm sure you find people to give you cuttings, which would root fairly easily; might even be time to get them established before winter. It's one tough vine.

Please Please Please come take as much of mine as you want! In my book, it is as bad as the buckthorn and grapes growing rampant in my back "yard". They all aspire to take over the world if given the chance....
It is quite pretty though- and can be managed, I assume, in smaller yards that get more attention-
Julie

I would pass on both. They both just start sprouting up all over once the birds start eating the fruit. And japanese beetles love the grape vines.