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