Will a grapevine grow successfully in a container?

Is it possible to grow a successful grape vine out of a container? I'd like to start a vine on my apartment balcony.
I don't know how deep the roots need to grow for this to work.

Oh yes you can! I have several growing just fine, but you do need a big pot, and you'll need to start again every few years (or use half - beer barrels).
This link tells you a bit more...
http://www.gardening-guides.com/pdf-libr...

You will need lots of water, especially if using an unglazed earthenware pot. You should protect the roots in winter from frost or prolonged cold - not much water in winter.

I have had no problems with mine, so give it a go. Temperate southern UK climate helps. I start mine off in small pots (6") for a couple of months to help them develop a good small root ball, then put them in a 10", 12" and 16" pot as they need it. Don't put them straight into a big pot - all the roots grow to the bottom, and most of the pot space is wasted. They need fertiliser on a regular basis (I use tomato fertiliser and follow the instructions there).
If you live in an apartment, make friends with the people above - the best of your plant may end up up there!!!

Happy growing and have fun!!

Star
Probably not, Hon....at least not for long.
Grapevines have a tremendous root system. Additionally, it you have cold winters, their roots would freeze in a pot. And as you probably know, their vines get extremely long and unwieldly, even with correct pruning.
If you'd like a vine growing on your balcony, you can grow Morning Glory (convolvulus), Thunbergia, Cobea, or any number of other annual vines successfully in a pot. Good luck :)