Season the chicken breasts with salt, pepper, and 1 - 2 Tbsp of the paprika.
Heat the oil in a large pot, sear the chicken breasts on one side, flip the chicken and add the onion and garlic.
Let the onions sauté slightly, sprinkle with the rest of the paprika, and some more salt and pepper and cover with water.
Bring to a boil, reduce heat and simmer until chicken is very tender (it can simmer up to a few hours, just add more water if it evaporates).
Right before you are ready to serve, remove the chicken from the liquid and keep warm.
To make the sauce, combine the sour cream and flour whisk until smooth. Once smooth, add some of the cooking liquid and whisk until there are no more lumps.
Pour the mixture back into the cooking liquid, and boil until it thickens (if it doesn't thicken enough, repeat the flour/sour cream/cooking liquid mixture until it has the consistency of thick gravy).
Remove bones from chicken breasts and cut into pieces and return to sauce.