A small amount will be fine, but if you try to add enough to make it significantly chocolate flavored, you'll throw off both the wet/dry ratio and the acid chemistry of the mix, and probably end up with an unsatisfactory cake.
Eggs are added to a cake primarily to help it rise, and to a limited extent to improve the moistness. The lecithin in the yolk also has emulsifying properties. For cakes, commercial egg replacers such as Ener-G will usually do the job nicely.
There's also a dairy product called QimiQ that's used in all manner of recipes to substitute for eggs, especially when a recipe needs raw eggs. It will also work well for cakes, although the substitution tends to be a little more involved. Also, it's probably harder to obtain.
I wouldn't substitute anything else in a cake. I've heard of people substituting all manner of things in other baked goods like cookies, but with a cake, you really need it to rise and you need the wet ingredients to bind together with the fats, and the only single "common" ingredient that will do that is either egg or a commercial egg substitute.
If you're literally about to bake this, as in you've got all your other ingredients already sitting in mixing bowls, and need to substitute the eggs with common ingredients you already have in your fridge or pantry, then I'm afraid you may have wasted your time (and your other ingredients). But maybe somebody else will have some suggestions - guess it can't hurt to wait, given the alternative.
Best Answer
There are a couple of cookbooks by Anne Byrn who has built a franchise on this subject. Her best known book (and the one I have) is titled The Cake Mix Doctor. written specifically on this subject.
Go to her website http://www.cakemixdoctor.com as there are several recipes and articles as well a listing of her books.