Rinse morilles and clean well. Place them in a medium size bowl and cover with water. Soak morilles in water for 30 minutes. Drain and discard water.
Place each breast half on an horizontal surface. With a sharp knife open each fillet lengthwise.
There will be 16 thin fillets. Season fillets with salt and pepper.
Melt butter with the oil in a large skillet. When butter has melted add fillets (in batches) and sauté on both sides over medium heat until almost done. Chicken will be slightly golden but will not have a hard crust. Add wine and bring to a boil for 3 minutes. Remove chicken breasts from the skillet as soon as they are done and keep them warm. Add onion to skillet and cook until tender. Stir in sherry bring to a boil and reduce for 3 minutes. Add morilles and mix. Stir in heavy cream, bring to a boil and reduce heat. Cook and reduce until sauce thickens lightly. Correct seasoning.
Serve over chicken fillets with vegetables.