What do you think that frozen cooked chicken in the supermarket is? It's cooked chicken which has been frozen. It's ok for you to do the same thing, assuming the chicken is not bad before you freeze it.
You can if it was deep-frozen raw chicken which was defrosted and then thoroughly cooked in the oven. If the cooked chicken is then deep-frozen it can be defrosted (thawed) and eaten, but should not be deep-frozen a third time.