Heat the oil in a large pot over medium-high heat. Season the chicken with ¼ teaspoon each salt and black pepper.
Cook the chicken until browned, 4 to 5 minutes per side. Remove from the pot.
Discard all but 2 tablespoons of the drippings. Add the onion, bell pepper, and garlic and cook, stirring, until tender, 4 to 5 minutes.
Add the tomatoes (crush them with your hands as you add them), paprika, ½ teaspoon salt, and ¼ teaspoon black pepper and bring to a boil.
Nestle the chicken in the vegetable mixture and simmer, partially covered, until cooked through, 15 to 20 minutes.
Meanwhile, cook the noodles according to the package directions. Top with the chicken, sour cream, and dill.