AFAIK you only get one chance at answering the chest's questions, though when you first talk to it you can put off the test (to save first, etc). There isn't anything special in the chest, though. I don't recall what I got, but it didn't seem like a great reward for getting the questions right on the first try. I saved and reloaded to see if you got less if you got an answer wrong (which you do, as the chest will not open then), or if I could get better random stuff trying again (nope; I think I got lowish level piece of equipment and a low/mid quality charm the first try, and something plus a potion the second).
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