Heat oil in a large skillet over medium-high heat. Add the chicken, season with salt and pepper, and cook until the chicken has browned, 10 to 12 minutes. Remove the chicken to a bowl.
Without cleaning the skillet, add the onion and bell pepper. Saute until browned. 4 minutes before the vegetables are done, add the mushrooms. Return the chicken to the skillet to reheat.
Heat broiler. Fill the rolls with the chicken mixture, top with the provolone, and place on a rimmed baking sheet. Broil until the provolone has melted, 2 to 3 minutes. Serve with french fries.