Put chicken carcass in large pot with enough water to cover, bring to a boil, cover and reduce heat and simmer for at least 1 hour. Remove carcass from broth and pick the meat from bones (it will literally fall off) set aside meat and broth
You should now have approximately 2 quarts of broth. If not, add water to make up the loss.
Melt butter in large pot and add flour stir constantly for 5 mins. Add onions/ celery, and carrots into roux and cook over medium heat for about 10 minutes.
Add broth, chicken, barley, and salt and pepper to taste.
Simmer on low for about 20 minutes. Add heavy cream and heat through.