Heat the oil in a 10-inch skillet over medium-high heat. Add the chicken and cook until well browned, stirring often.
Reduce the heat to medium. Add the pepper and onion to the skillet and cook until the vegetables are tender-crisp, stirring occasionally. Stir in the soup and salsa and cook until the chicken is cooked through.
Spoon about 1/2 cup chicken mixture down the center of each tortilla. Top with the cheese and additional salsa. Fold the tortillas around the filling.