Heat oil in a medium skillet over medium-high heat. Add chicken breasts and saute until tender. Meanwhile, prepare potatoes according to package directions, adding 1 cup (instead of 2/3) of milk and sliced potatoes. When chicken is tender, remove from heat, let cool and shred. Add shredded chicken to potato mixture.
Fold chicken/potato mixture into 9x13-inch baking dish. Cover and bake in a preheated oven for 25 to 35 minutes. Add cheese and bake for another 10 minutes.