Preheat the oven to 325°F (165°C). Place chicken breasts in a single layer in a 9x13-inch baking dish.
In a saucepan over low heat, melt butter. Stir in Italian dressing mix, condensed mushroom soup, and cream cheese. Cook until smooth and creamy, stirring often.
Pour the sauce over the chicken. Bake for 1 hour, or until chicken reaches 165°F (74°C).
About 15 minutes before the chicken is done, bring salted water to a boil. Cook angel hair pasta for 4–5 minutes until al dente. Drain well.
Plate pasta, top with chicken and sauce, and garnish with parsley if desired.