Wash the asparagus, cut off the woody ends. Cut thick asparagus spears in half lengthwise. Wash the meat, dab dry and season with salt, pepper and paprika. Heat 1 tablespoon of oil in a frying pan.
Fry the chicken fillets for about 8 minutes, turning them over. In the meantime heat 1 tablespoon of oil in another large frying pan. Fry the asparagus in 2 portions for 4-5 minutes and season with salt. Wash tarragon, shake dry and chop half of the leaves into small pieces.
Peel and finely dice the shallot. Melt butter in a small pot. Sauté the diced shallots for about 1 minute, then deglaze with white wine, cream and stock. Add whole tarragon leaves and simmer for about 3 minutes.
Puree the sauce and thicken with sauce thickener. Bring to the boil and season to taste with salt, pepper and possibly a little sugar. Remove meat from the pan and cut into slices. Arrange asparagus spears and chicken fillets and drizzle with the sauce.
Cut the remaining tarragon into strips and sprinkle over the sauce.