Bring first 7 ingredients to a boil in a large Dutch oven; cover, reduce heat, and simmer 45 minutes or until chicken is tender. Remove chicken, reserving broth in Dutch oven. Let chicken and broth cool. Skin, bone, and cut chicken into bite-size pieces; set aside. Skim fat from broth. Add soup to broth; bring to a boil.
Cut tortillas into 2- x 1-inch strips. Add strips, 1 at a time, to briskly boiling broth mixture. Add chicken, reduce heat, and simmer 10 minutes, stirring often to prevent dumplings from sticking.
Quick Tip: Substitute 8 cups chicken broth for water; omit bouillon cubes; reduce salt to 1/2 teaspoon. Proceed with recipe using 3 to 4 cups chopped cooked chicken.