Melt lard in a chicken fryer or heavy, deep kettle. Heat to 250 degrees. Fry chicken pieces a few at a time for 20 minutes. Keep fried chicken warm while frying remaining batches. Add paprika to taste.
Process tomatoes briefly in a blender.
Add tomatoes, rice, salt and pepper to onion mixture. Cover and cook until rice is tender, about 45 minutes, adding additional water if necessary. Remove pepper slices before serving. You should have about eight cups. Combine vinegar, oil and sugar and whisk until sugar has dissolved.