It's not near as good as a chuck roast but it can be braised. There are some recipes out there. Be warned that some people can get very adamant about braising "eye of round". Here is a link to another Chowhound thread on the subject. http://chowhound.chow.com/topics/7338...
Most people roast that particular cut. It is not considered a very good candidate for braising because it is a lean cut. However, some people braise them and like their results.
There is a recipe or two in that old thread.
After reading the rules, I think I'm allowed to post this here. If not, it will magically disappear I suppose.
This will explain the differences between the roasts. You could roast it or braise it, generally braising is better for fattier cuts, which the round isn't. "Eye" means it's from the middle of the cow, afaik. Chuck = shoulder back to first 5 ribs, and round is from the legs and back areas. Just going by memory of what I read tonight, could be wrong. Good luck!
Also see: http://www.cooksillustrated.com/image...