Place the chicken breasts in a glass or non-reactive baking dish.
Stir the onion soup mix, cranberry sauce, and French dressing together in a bowl until well blended. Pour over the chicken breasts. Cover the baking dish with plastic wrap, and refrigerate at least 8 hours.
Preheat oven to 350 degrees F (175 degrees C).
Remove plastic wrap from the baking dish, and cover loosely with aluminum foil.
Bake chicken in preheated oven until top is bubbly and slightly browned, about 1 hour and 15 minutes.