Heat gas or charcoal grill. Cut one 14x12-inch piece of heavy-duty foil. Spray one side generously with cooking spray.
In small bowl, pour oil over potato pieces; toss to coat. Add chives and garlic salt; toss to coat. Sprinkle with cheese; toss to coat.
Place potatoes on center of sprayed side of foil piece. Fold foil over potatoes so edges meet. Seal edges, making tight 1/2-inch fold; fold again. Allow space on sides for circulation and expansion.
Cover and grill packet over medium-low heat 15 to 20 minutes, turning once, until potatoes are golden brown and tender.