Preheat your oven to 325°F (165°C). Arrange chicken breasts in a single layer in a 9x13-inch baking dish.
In a large saucepan, melt the butter over low heat. Stir in the Italian-style salad dressing mix until combined.
Add the condensed golden mushroom soup, stirring until smooth. Fold in the cream cheese with chives, cooking gently until the mixture is well mixed and heated through. Do not let it boil.
Pour the creamy sauce over the chicken breasts, ensuring they're evenly coated.
Bake the chicken in the preheated oven for about 1 hour, or until the meat reaches an internal temperature of 165°F (74°C).
Approximately 15 minutes before the chicken is finished, bring a large pot of salted water to boil. Cook the angel hair pasta for 4-5 minutes, or until al dente. Drain well.
Serve the baked chicken and creamy sauce over the cooked pasta. Garnish with fresh parsley if desired.