In a food processor grind the walnuts and garlic. Add 1 tablespoon cold water to help. Season with salt and pepper and slowly beat in the oil until you have a thick sauce almost like a mayonnaise. Stir in the parsley.
Marinate the chicken breasts in the yoghurt, seasoned with salt, pepper and lemon juice for 1/2 hour. Wipe off surplus yoghurt.
Heat some oil in a frying pan and pan fry the chicken for about 3 minutes each side to sear. Spoon over the aillade (walnut sauce) and cook over low heat until chicken is done.