Lightly coat your slow cooker with nonstick spray. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Season the chicken with salt and pepper.
Add about 1/2 tablespoon more of olive oil if needed, then add the chopped onion. Sauté for 3 minutes until softened. Stir in minced garlic and balsamic vinegar and cook for 1 minute.
Add the crushed tomatoes, chopped green bell pepper, sliced mushrooms, and Italian seasoning, dried oregano, and dried thyme to the chicken and veggies in the slow cooker.