Flatten chicken breast halves to 1/4-inch thickness between two sheets of heavy duty plastic wrap.
Heat the olive oil a large skillet with a tight-fitting lid over medium heat; add chicken and brown on each side.
Combine barbecue sauce and hot pepper sauce; pour over chicken, turning to coat. Cook for about 15 minutes, turning once, until chicken is no longer pink in the center.
A few minutes before removing from heat, sprinkle each chicken breast half evenly with shredded Mozzarella cheese; cover skillet to melt cheese.