Place a large Dutch oven over medium-high heat and add a film of olive oil. Sprinkle the chicken on both sides with salt and pepper and then add to the pan skin-side down. Cook without moving too much until golden brown and crisp, 5 to 6 minutes. Flip and brown on the other side for 1 to 2 minutes. Remove to a plate and set aside.
Drain half of the fat from the pan and then place it back over the heat. Add the sausage to the pan, breaking it up as you add it. Brown for 1 to 2 minutes while continuing to break it up with the back of a spoon. Stir in the onions, peppers and garlic with a pinch of salt and cook until the onions begin to soften, about 3 minutes. Season with salt and pepper and then add the tomatoes, chicken stock and oregano, scraping the bottom of the pan for brown bits.
Nestle the chicken back in, cover and cook until the chicken is cooked through and the sauce has thickened, 20 to 30 minutes.