Heat closed medium-size contact grill for 5 minutes; spray grill plates with cooking spray. In medium bowl, mix chicken, 1/3 cup of the salsa and the cheese.
Press each biscuit into 5-inch round. Place 1/4 cup chicken mixture on one side of each round. Fold dough over filling; press edges with fork to seal.
Place 2 biscuits at a time on grill; close grill. Cook 2 to 3 minutes or until golden brown. Cut each quesadilla into 3 wedges; serve with remaining salsa.