Soak a package of bamboo skewers in warm water for 20 to 30 minutes; drain. Preheat grill to medium-high.
Thread 3 pieces of chicken on each skewer. Brush chicken with olive oil and sprinkle with salt and pepper. Douse a paper towel with vegetable oil and, holding it with tongs, carefully oil grill grate (or, away from heat, mist grill grate generously with nonstick cooking spray). Arrange chicken skewers on grill so that they are not touching. Cover grill. Grill chicken until cooked through, 6 to 8 minutes, turning once. Serve hot or at room temperature. Or let them cool, cover with plastic wrap and refrigerate to serve later.