Heat butter and oil in a Dutch oven over medium heat; add the onions and cook until translucent.
Sprinkle the chicken with kosher salt and fresly ground black pepper; add to the onions and brown lightly, turning to brown all sides.
Add the bell pepper, garlic, tomatoes, and paprika.
Add the broth (or water) and bring to a boil. Reduce heat to low, cover and cook for 30 to 40 minutes or until chicken is tender. If you are using only chicken breasts, check the temperature after 20 minutes. 165 F is the minimum temperature for chicken, but dark meat—thighs, legs, and wings, are best cooked to at least 175 F.
Remove the cooked chicken to a heated platter and tent with foil to keep it warm.
Reduce the heat under the Dutch oven to low.
In a small bowl, whisk together sour cream and flour. While whisking constantly, add a few tablespoons of the hot broth from the Dutch oven.
Stir the sour cream mixture into the Dutch oven juices and bring to a simmer. Do not boil.
Return chicken to the pan and heat just long enough to rewarm.
Serve chicken paprikash over noodles, spaetzle, rice, or potatoes.