Marinate the chicken at least 4 hours, overnight is even better.
When ready to cook, thread the chicken on skewers. Discard marinade.
Prepare grill for direct cooking. Brush the grates with a little oil and grill the skewers, turning often, for about 5 minutes total. An instant-read thermometer should read 155°-160°. The internal temperature will continue to climb for a few minutes, even off the heat. Let the souvlaki rest for several minutes before serving.
Serve with pita or rice, vegetables, and tzatziki sauce.
