Combine first 6 ingredients in a Dutch oven; bring to a boil. Cover, reduce heat, and simmer 40 minutes or until chicken is tender. Remove chicken from cooking liquid; cool. Remove meat from bones, and chop. Strain mixture through a sieve into a large bowl; reserve 4 1/2 cups. Reserve remaining broth for another use.
Heat oil in pan over medium-high heat. Add onion and next 3 ingredients; sauté 10 minutes or until tender. Stir in chicken, reserved broth, rice, and remaining ingredients; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until rice is tender.