Set a 5- to 6-quart pan over medium-high heat. When pan is hot, add oil, onion, and salt. Lower heat to medium and stir occasionally until onion is translucent, 3 to 5 minutes.
Add chicken pieces. Cook, covered, for about 10 minutes.
Add green pepper, tomato, and paprika. Stir, then cook, covered, over low heat for 30 to 40 minutes, until the chicken is no longer pink in center. Remove chicken.
Skim fat from pan and increase heat to medium-high. Cook uncovered until liquid is reduced to 1 1/2 cups, about 15 minutes.
Stir cornstarch into the sour cream. Add mixture and chicken to pan and cook, uncovered, 5 to 10 minutes, until everything is hot and the sauce has thickened.