Peel the eggs and cut in half. Put the yolks in a bowl and mash with a fork with mayonnaise and hot sauce. Chop the chicken very finely. Grate carrots on a fine grater. Cut the celery into small cubes. Finely chop the chives.
Add vegetables and chicken to yolks, add cheese and stir. Fill egg halves with mixture and garnish with parsley.