Cheesy Broccoli Chicken Soup

Cheesy Broccoli Chicken Soup
4-6 chicken breasts
3 large diced carrots
3 stalks celery, chopped
1 onion, diced
1/2 cup butter or margarine
1/2 cup flour
1 qt. half and half (can do 2 cups milk, 2 cups half and half)
2 cups chicken broth
1/2 lb fresh broccoli cut into pieces, or 2 10 oz packages frozen broccoli
1- 16 oz package velveeta cheese, cut into cubes
Boil chicken, carrots, celery, and onions until done. Remove chicken and vegetables and save 3 cups of the broth. Cube the chicken and set aside. Discard the rest of the broth. In a pot melt butter and stir in flour. Slowly add broth and half and half. Heat until thick. Add the velveeta cheese and stir until melted. Add chicken and vegetables.  Heat thouroughly and enjoy.