Bring first five ingredients to a boil in a Dutch oven over medium-high heat, stirring often. Separate biscuits in half, forming 2 rounds; cut each round in half. Drop biscuit pieces, one at a time, into boiling mixture; stir gently. Cover, reduce heat to low, and simmer, stirring occasionally, 15 to 20 minutes.

One roasted whole chicken or six skinned and boned cooked chicken breast halves yield about 3 cups chopped meat.