Do you have to wait for chicken cool down before refrigerate it?

Yes.

Cooked chicken should be cooled within two hours of cooking, and then refrigerated.

This will help to prevent the growth of bacteria.

To cool chicken quickly, you can place it in an ice water bath or shallow dish of ice cubes.

Stir the chicken occasionally until it has cooled down.

Once the chicken has cooled, transfer it to an airtight container and refrigerate it.