Trim excess fat from thighs. Cut each thigh lengthwise into 1 1/2-inch-wide strips. Reserve and chill 1/4 cup of desired marinade. Place chicken and remaining marinade in a large zip-top plastic freezer bag. Seal and turn bag to coat. Chill, turning bag occasionally, 3 to 8 hours.
Meanwhile, soak wooden skewers in water 30 minutes. Preheat grill to 350° to 400° (medium-high) heat. Remove chicken from marinade, discarding marinade. Pat chicken dry with paper towels. Thread 3 chicken strips in a loose accordion style onto each skewer. Brush with vegetable oil, and sprinkle with salt and pepper.
Grill kabobs, covered with grill lid and turning occasionally, 11 to 14 minutes or until chicken is done. During last 5 minutes of grilling, brush kabobs with reserved 1/4 cup marinade.