Place the chicken thighs in the slow cooker. Add the sliced onion, bell peppers, and minced garlic on top.
Pour the diced tomatoes and 1 cup chicken broth over the vegetables. Sprinkle in the oregano, basil, salt, and pepper.
Cover and cook on low for 6 to 7 hours until the chicken is very tender.
About 20 minutes before serving, bring the remaining 4 cups chicken broth to a boil in a saucepan. Slowly whisk in the cornmeal.
Reduce heat to low and cook the polenta for 15 minutes, stirring often until thick and creamy. Stir in the olive oil, parsley, rosemary, and Parmesan cheese.
Taste the cacciatore sauce and adjust salt if needed. Serve the chicken and sauce over scoops of the herbed polenta.