Trim chicken of excess fat and cut into approximately 1-inch wide pieces. Set aside.
Combine all marinade ingredients in a medium-size bowl and stir to mix. Add chicken to a large zip lock bag along with half of the marinade/sauce. Reserve the remaining marinade and set aside.
Massage the bag with the chicken to evenly coat the chicken with marinade. Refrigerate for at least 30 minutes and up to 4 hours.
Heat a gas grill to medium-high or start a medium-hot charcoal grill. Thread chicken onto skewers (if using wooden skewers, soak them in water for at least 30 minutes, so they don't catch on fire.)
Clean grill surface and oil with spray or brush with a tongs and an oil-dipped paper towel. Place skewers on grill and cook, turning one-quarter turn every 3-4 minutes until golden, about 10-12 minutes. Brush with the remaining sauce, turning frequently until chicken is charred in spots. Exact timing will vary, depending on the temperature of your grill. Remove the chicken skewers from the grill, tent with foil and let rest for 5 minutes.