Season the chicken pieces with salt and pepper. Heat the vegetable oil in a large skillet or pot over medium-high heat.
Add the chicken to the pan and cook until browned on all sides. Remove the chicken from the pan and set aside.
In the same pan, add the chopped onions and garlic. Sauté until the onions are translucent and fragrant.
Stir in the sweet paprika, making sure it coats the onions evenly. Cook for another minute to release the flavors.
Add the sliced bell peppers to the pan and cook for a few minutes, until they start to soften.
Return the chicken to the pan and add the diced tomatoes and chicken broth. Stir well to combine.
Reduce the heat to low, cover the pan, and let the chicken simmer for about 30-40 minutes, or until the chicken is cooked through and tender.
Stir in the sour cream, allowing it to blend with the sauce. Cook for an additional 5 minutes until heated through.
Taste and adjust the seasoning with salt and pepper if needed.
Serve the chicken paprikash over cooked noodles or rice, garnished with freshly chopped parsley if desired.