Generously season the chicken with salt & pepper and then coat it in flour (and shake off any excess).
Add the oil and butter to a Dutch oven/soup pot/braiser over medium-high heat for a few minutes, then add the chicken and sear for 3-4 minutes/side or until golden. Transfer the chicken to a plate.
Add in the onions and cook for 3 minutes.
Add in the carrots and red bell pepper and cook for 5-7 minutes, stirring occasionally.
Stir in the garlic and cook for 30 seconds.
Add in the white wine and crushed tomatoes and scrape up any browned bits from the bottom of the pot.
Stir in the thyme and oregano.
Add the chicken back in and spoon some sauce over top. Cover the pot with the lid slightly ajar, reduce the heat, and gently simmer (turn the heat way down) for at least 20 minutes or until the carrots have softened and the chicken is tender (you can stir halfway through if you wish). The sauce will thicken up a bit. If it becomes too thick, add a splash more wine or chicken broth.
Season with salt & pepper as needed, and stir in the Kalamata olives, basil, and parsley.