a nice filipino condiment to make if you have an unripe papaya is "achara"... goes great with phillipine style BBQ or similair meat dishes.
grate two big green papayas and then finely slice a raw onion, a carrot or two, and a red pepper. in a pot, bring 3 1/2 cups vinegar to a boil with about 1/4 cup sugar and some salt. add the papaya, and simmer for a few minutes, then add the other ingredients and simmer some more, about 20 minutes total. add a small amount of whole black peppercorns and then put the whole thing in your fridge overnight. spicy, sour, and a little bit sweet.
your papaya is probably ripe.. but maybe next time. i dont really like papaya fresh, but i love this stuff.