Yes chicken or any other meat can be refrigerated after cooking it.
You can also freeze the cooked chicken or any other meat that you've cooked and it will be just fine.
You should always refrigerate or freeze any leftover chicken or other meats to prevent the potential of bacteria growing on the chicken or meat which can potentially cause you to be sick.
I've refrigerated leftover chicken before because sometimes I'll cook too much chicken and then have leftover chicken which then gets either frozen or refrigerated to eat later.
Many people including myself have refrigerated chicken after cooking and you can put the chicken in the refrigerator even when it's still hot and it will be okay.
The refrigerator will cool the chicken down once you refrigerate it.