Though it is more expensive than other Chuck cuts, it will turn out a very good roast beef, provided you are not looking for picture-perfect rare roast beef with pink in the middle.
Chuck Eye makes one of the best pot roasts; some people feel that it performs reasonably well as an dry-oven roast (those people must like chewing.)
If you want to grind your own hamburger, Chuck Eye is a good choice of meat to start with as it is tough and fatty enough to make good minced beef.
Whether being used as a pot roast or as stewing beef, it will start to fall apart on you if you cook it as long as you would other chuck meats.
Eye of Round roast.