In a large enameled cast-iron casserole or Dutch oven, heat the oil until shimmering. Add the onion, bell peppers and garlic and cook over moderate heat, stirring occasionally, until just beginning to brown, about 8 minutes. Add the paprika, caraway and flour and cook, stirring, for 2 minutes. Add the stock, bay leaves and thyme sprigs, season with salt and pepper and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the peppers are very tender and the sauce is thickened, about 1 hour.
Add the chicken to the sauce and cook over high heat until just white throughout, about 6 minutes. Discard the bay leaves and thyme sprigs. Spoon the chicken into bowls, and top with sour cream. Sprinkle with paprika and serve.