Place chicken breasts on the baking sheet and sprinkle with 3/4 of the ranch dressing packet.
Bake chicken in the preheated oven until lightly browned and the juices run clear, about 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Remove from oven and spoon Cheddar cheese soup over the chicken breasts. Sprinkle with remaining ranch dressing mix.
Place asparagus spears on the chicken breasts.
Top each chicken breast with a slice of Swiss cheese.
Return chicken to oven and bake until the asparagus is slightly tender and the cheese is hot, about 15 more minutes.