Grease a flat ovenproof dish. Clean the snow peas and blanch them in boiling salted water for about 2 - 3 minutes. Quarter the tomato and remove the stone. Finely dice the pulp. Drain the snow peas on a sieve and place in the mold.
Heat a pan with oil and fry the fillets vigorously for about 8 minutes, turning them. Season with salt and pepper, remove from the pan and place on the sugar snap peas. Deglaze the roast set with cream, bring to the boil and stir in the sauce thickener. Let it boil again briefly.
Stir the pesto into the cream and season with salt and pepper. Pour the pesto cream over the chicken fillets and sprinkle with diced tomatoes. Bake in a preheated oven (at 200 °) for 10-15 minutes.
Meanwhile, cook the pasta in salted water as usual and drain. Arrange the chicken fillets with the ribbon noodles on plates.