Line a large plate or baking sheet with paper towels. In a large skillet, heat the oil until shimmery and hot but not smoking, Fry the tortillas one at a time until firm but not burned, about 1 minute per side. Transfer to the paper towels and let cool for 5 minutes.
Place the lettuce, cheese, sour cream, tomato and avocado in separate serving bowls.
Spread the refried beans on each of the tortillas. Sprinkle the shredded chicken on top of the beans. Arrange the chalupas on a platter and serve them with the serving bowls of toppings so everyone can build their own!