Preheat the oven to 350 degrees.
Brush the chicken with oil and sprinkle with salt and pepper. Grill the chicken on the stovetop griddle. Over medium high heat, this takes about 5 minutes per side (timing may vary according to thickness of chicken). The chicken is cooked through when it reaches an internal temperature of 165 degrees. Set aside the cooked chicken to cool a bit, then shred it with two forks.
In 2 large oven-safe dishes (e.g. cast iron pans, 9 by 13 inch glass baking pans), divide the tortilla chips between the two pans. Top with the chicken. Add dollops of refried beans and sprinkle with cheese. Cover the baking dishes with foil and bake for 15 minutes, or until the cheese is melted. Remove the foil and bake for another 2 minutes.
While the tortilla chips and chicken mixture are baking, prepare the remaining toppings. As soon as the tortilla chip pans come out of the oven, top with the carrots, olives, salsa, and lettuce. Serve warm.