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 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.