In a wide pot, place the pork fat over medium heat.
Once heated, add the chicken pieces (in batches if they won't fit in a single layer) and brown on all sides.
Remove the chicken to a plate and set aside.
Add the onions to the pot and cook, stirring occasionally, until softened. Stir in the garlic.
Remove the pot from heat and stir in the paprika.
Add the tomato, bell pepper, and water, then return the pot back to medium heat.
Add the chicken pieces and pour in just enough water to barely cover the chicken. Season with the salt.
Once the liquid comes to a boil, reduce heat to a very low simmer, cover, and cook for an hour, until the chicken is cooked through and tender. Season to taste if needed.
Serve the Csirkepörkölt hot with sour cream and parsley if desired.