Pat the chicken thighs dry with paper towels. Season them evenly with ½ teaspoon salt and ¼ teaspoon black pepper. Dredge each piece lightly in the flour, shaking off any excess.
Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Once hot, add the chicken thighs skin-side down. Cook for about 5-6 minutes per side, or until the skin is golden and crispy. Remove the chicken from the pan and set aside.
In the same pan, add the diced onion and sliced carrot. Sauté for about 4 minutes until they start to soften. Add the mushrooms and cook for another 3 minutes until they release their moisture and begin to brown. Stir in the minced garlic and cook for 1 more minute until fragrant.
Add the red and yellow bell pepper strips to the pan, stirring to combine. Sprinkle in the dried oregano, thyme, basil, the remaining ½ teaspoon salt, and ¼ teaspoon black pepper. If you like a little heat, add the crushed red pepper flakes now. Cook for 2 minutes to allow the flavors to meld.
Pour in the red grape juice to deglaze the pan, scraping the bottom with a wooden spoon to lift all the flavorful browned bits. Let the red grape juice simmer for about 3-4 minutes until it reduces slightly.
Stir in the diced tomatoes and tomato paste until well combined. Bring the sauce to a gentle simmer.
Nestle the browned chicken thighs skin-side up into the sauce. Cover the pan with a lid and let it simmer gently over low heat for 35-40 minutes, or until the chicken is cooked through and tender.
About 5 minutes before serving, stir in the pitted black olives. Let the sauce simmer uncovered to thicken slightly and allow the olives to warm through.
Serve your Chicken Cacciatore hot over cooked pasta, rice, or creamy polenta. Garnish with fresh herbs if desired, and enjoy!