In lg skillet, heat oil over med-high heat. Add chicken and cook about 10 mins, turning once, until browned. Remove chicken to a platter.
Drain all but 1 tbsp drippings from pan. Add mushrooms to pan and cook until soft, about 5 mins. Stir in milk and sauce packet. Arrange chicken in 1 layer over mushrooms. Reduce heat. Cover, simmer 10 mins, stirring occasionally.
Stir in peas and cook 4 mins. Fill a 2-quart saucepan 1/2 full of water. Bring to a boil. Stir in pasta from stroganoff box. Boil, stirring occasionally, until pasta is tender. Drain. Place pasta on lg platter. Top w/ chicken, sauce, mushrooms and peas.