Heat olive oil in a large skillet over medium heat. Season chicken with sea salt and freshly ground pepper and brown in the skillet until golden, starting skin-side down, about five minutes each side. Brown chicken in batches, if necessary. Remove chicken from skillet to a plate and set aside.
Remove all but 2 tablespoons of fat from the skillet; add onion, bell peppers and garlic and sauté over medium heat about 3 minutes. Add diced tomatoes in their juices, paprika, chiles ancho, thyme and bay leaf and return the reserved chicken, with any collected juices, to the skillet. Season with sea salt and freshly ground pepper, cover and let simmer over low heat for 50 minutes.
Stir in the diced prosciutto and continue to cook uncovered until the chicken is done, about 10 minutes.
Divide chicken among four shallow bowls. Using a slotted spoon, top the chicken with bell pepper strips and prosciutto and spoon remaining sauce around each serving of chicken. Serve immediately with crusty bread.