Sear the chicken: Heat olive oil in a large skillet over medium-high heat. Brown the chicken on both sides for about 5 minutes per side. Remove and set aside.
Sauté the vegetables: In the same skillet, add the onion, garlic, bell pepper, and carrot. Cook for 5 minutes until softened.
Add the wine: Pour in the red wine and let it simmer for 2 minutes to deglaze the pan.
Prepare the sauce: Add crushed tomatoes, chicken broth, salt, pepper, oregano, basil, and red pepper flakes. Stir well.
Simmer the chicken: Return the chicken to the pan, cover, and let it simmer on low heat for 40 minutes. Stir occasionally.
Finish and serve: Stir in olives (if using), let cook for another 5 minutes, then garnish with fresh parsley. Serve with pasta, rice, or crusty bread.