Sprinkle salt and pepper over both sides of chicken. Using your fingertips, gently press the seasonings so they adhere to the chicken.
In a large nonstick skillet, heat the oil over medium high heat, swirling to coat the bottom. Cook the chicken for 3-5 minutes on each side, or until browned. Transfer the chicken to a large plate. Set aside.
Chops onions and mince garlic. Place onions and garlic in the bottom of the slow cooker.
Slice peppers into strips and stir into slow cooker.
Arrange chicken on the onion mixture. Don’t stir. Sprinkle with rosemary and Parmesan cheese. Cook on low for 3-5 hours or on high for 1 1/2 to 2 1/2 hours or until chicken is no longer pink in the center.
Cut zucchini into rounds, add to the slow cooker the last hour of cooking.
Serve the chicken topped with the veggie mixture. Spoon the cooking liquid onto the chicken.