Bring first 3 ingredients to a boil in a Dutch oven; cover, reduce heat, and simmer 30 to 35 minutes or until chicken is tender. Remove chicken, reserving broth in Dutch oven; let chicken cool. Bone and cut chicken into bite-size pieces.
Place biscuits on a floured surface; roll or pat to 1/8-inch thickness. Cut biscuits into thirds.
Bring broth to a boil. Drop biscuits, 1 at a time, into boiling broth; add chicken. Cook, stirring occasionally, 10 minutes.
Quick Tip: Substitute 6 cups reduced-sodium chicken broth for water; use 3 cups chopped cooked chicken.