Preheat the oven to 180 degrees. Halve the chicken breast fillets lengthways. Break off the woody ends of the asparagus. Mix the oil with the sugar and the fish sauce. Place the fillets and asparagus in the seasoned oil and rub well.
Put everything in a deep baking dish. Cook in the oven (middle shelf) for about 40 minutes. Turn everything once halfway through the cooking time. Just before the end of the cooking time, sprinkle the paprika over the fillets.