Place the frozen chicken breasts into a slow cooker, and arrange the mushroom caps on top of the chicken so that about half the mushrooms are facing up. Drizzle the dressing over the chicken and mushroom caps.
Place the lid on the slow cooker, turn it to the Low setting, and cook until the chicken breasts are no longer pink at the bone and the juices run clear, about 6 hours.
A few minutes before serving, fill a large pot with lightly salted water and bring to a rolling boil over high heat. Stir in the angel hair pasta, and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, 4 to 5 minutes. Drain well in a colander set in the sink.
Divide the hot, cooked pasta among four plates, top each plate with a chicken breast and two mushroom caps, and drizzle sauce over the top.