Season chicken pieces with salt and pepper.

Heat a Dutch oven or large braising pan over medium heat. Add olive oil to the pan and heat; working in batches, brown the chicken pieces about 3 minutes on each side. Remove the chicken from the pan; set aside.

To the same pan, add diced onion and pepper and sauté for 5 minutes. Then add the mushrooms and continue to sauté for another 3 minutes. Add in the grated garlic, capers, and oregano; stir constantly for 1 minute.

Stir in wine, cook for 3 minutes scraping up any brown bits from bottom of pan.

Add diced tomatoes (with liquid), chicken broth and bay leaf; bring to a low boil. Salt and pepper to taste.

Return the chicken pieces to the pan and turn them to coat in the sauce. Bring the sauce to a simmer. Continue simmering over medium-low heat until the chicken is just cooked through, about 40 minutes for the breast pieces, and 25 minutes for the thighs. Or, you can cook it up to 2 hours.

Using tongs, transfer the chicken to a platter. If necessary, boil the sauce until it thickens slightly, about 3 minutes. Spoon off any excess fat from atop the sauce. Spoon the sauce over the chicken, then sprinkle with the basil and serve.