Season chicken with salt and pepper. Warm oil, In a 5 1/2 quart dutch oven over medium-high heat. Add Chicken; brown on all sides, about 7 minutes total. Transfer chicken to plate.
Reduce heat to medium. Add onion; cook until softened, about 3 minutes. Add garlic; cook 2 minutes more. Add squash, wine, 2 tbs parsley and 2 tsp tarragon. Cook, stirring occasionally, until squash is soft but not browned, about 4 minutes.
Return chicken to pan; add tomatoes, olives and stock. Bring to a gentle simmer; reduce heat to low. Cover and simmer until chicken is cooked through, 25-30 minutes. Stir in 1 tbs parsley and teaspoons tarragon. Serve immediately.