Heat gas or charcoal grill. In medium bowl, stir together cheese, olives, onions and oregano. Place chicken breasts flat on cutting surface. Cut a lengthwise slit in each chicken breast forming a pocket, keeping other 3 sides intact. Stuff each chicken with cheese mixture; secure with toothpicks. Brush chicken with oil; sprinkle with salt and pepper.
Place chicken on grill over medium heat. Cover grill; cook 8 to 10 minutes, turning occasionally, until juice of chicken is clear when center of thickest part is cut (170°F).