In a large heavy saucepan over medium heat, bring chicken broth and water to a simmer. Add the chicken, carrots, celery and onion, parsley and pepper. Cover and cook until chicken is tender, about 20 minutes. Remove chicken and set aside.
Stir the escarole and tomato into saucepan and simmer uncovered for 5 to 10 minutes. When chicken is cool enough to handle, cut into 1/2 inch cubes, return it to the saucepan and bring soup to serving temperature.