Cook onion with salt in fat in pot over moderately high heat, covered, stirring occasionally and reducing heat if necessary, until onion is very tender but not browned, about 5 minutes.
Add paprika and cook, stirring, 1 minute. Stir in tomatoes and broth, stirring vigorously to break up tomatoes. Add chicken and simmer, meat side down, covered, stirring occasionally, 10 minutes. Simmer, uncovered, until chicken is just cooked through, about 5 to 10 minutes longer. Remove the chicken from the sauce and keep warm.
Stir flour mixture and stir into sauce. Simmer, stirring, until sauce is slightly thickened, about 2 minutes.
Remove from heat, then season with salt and stir in 2 tablespoons sour cream. Add chicken back to the sauce to warm and coat with the sauce. Serve, sprinkled with parsley, over noodles or rice, with additional sour cream on the side.
Cooks' note: Chicken can be prepared, without the sour cream, 2 days ahead and cooled, uncovered, before chilling, covered.