Generously season both sides of chicken with the 2 teaspoons salt and 1/2 teaspoon pepper, set aside.
Cook 5-6 slices chopped bacon until browned and crisp over medium heat in a large Dutch oven or other heavy-bottomed pot with a lid. Remove bacon from pan and add the 2 tablespoons olive oil. Once shimmering, add half of the chicken pieces and cook on one side until well browned. Flip and repeat on other side, remove from pan to a clean plate and repeat with remaining chicken.
Add 1 chopped shallot, 2 chopped carrots, 1 chopped celery stalk, and 8 ounces sliced mushrooms to pan and season generously with salt and pepper. Cook, stirring occasionally, until vegetables start to brown, about 10 minutes. Add 1 teaspoon smoked paprika and stir to incorporate into veggies. Add 1 cup red wine and scrape up any browned bits stuck to the bottom of the pan.
Add 15-ounce can tomatoes, 2 teaspoons capers, 1 cup chicken broth, the chicken and the cooked bacon and bring to a boil. Reduce heat to a slow simmer, cover and cook until chicken is tender, at least 30 minutes. Taste and season with additional salt and pepper if needed.