Preheat the oven to 325 degrees F (165 degrees C). Arrange chicken breasts in a single layer in a 9x13-inch baking dish.

Melt butter in a large saucepan over low heat. Stir in dressing mix, then stir in condensed soup and wine. Add cream cheese; cook and stir, without boiling, until smooth and heated through. Pour over chicken.

Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 1 hour. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

About 15 minutes before the chicken is finished, bring a large pot of lightly salted water to a rolling boil. Add angel hair pasta and cook, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes. Drain.

Serve chicken and sauce over pasta.