Can I freeze meat again after I thawed it?

Hey all, I made some chicken tonight for supper... I stuck it right in the freezer after I bought it and didnt get the chance to separate it. So I took it out, zapped it in the microwave, ran it under some warm water, etc etc just to get it loosened up enough to break three off of the block. It was mostly still frozen all the way through, and I put the rest of the chicken back in the freezer as soon as I broke off what I needed... what do you think, are the other frozen s still good to eat? (Sorry but just learning this cooking thing... i just started college.) thanks.