Heat margarine in a skillet over medium heat; stir in onion
Cook and stir until onion has softened and turned translucent, about 5 minutes
Reduce heat to low and continue to cook and stir until onion is very tender and dark brown, about 40 minutes more
Bring chicken broth to a boil in a large pot; stir in chicken breasts, reduce heat, and simmer until chicken is no longer pink at the center, about 20 minutes
Remove from heat
Remove chicken breasts to a plate using a slotted spoon; reserve broth
Juice potatoes with an electric juicer; place dry potato flesh into a bowl and discard juice
Stir salt and pepper into potatoes; stir in enough reserved broth to make the mixture the consistency of oatmeal
Set remaining broth aside
Spread half of potato mixture evenly into the prepared pan
Lay cooked chicken breast evenly over potatoes; scatter caramelized onion evenly over chicken
Spread remaining potato mixture over onions and chicken to cover
Bake in the preheated oven until golden brown, about 1 hour
Reheat chicken broth; pour over individual servings as desired