Mix the chicken and marinade together very well. Let marinate for at least 4 hours, ideally overnight and up to 24 hours.
The ideal way to cook the chicken is on a grill heated to medium (you can keep your hand hovering 3 inches over the grates for about 4 seconds). Remove the chicken from the marinade and discard the marinade. Grill turning every 3 minutes or so until cooked through and registers about 160 F on an instant meat thermometer. Thighs are very forgiving but be very vigilant if you are using chicken breasts so that they do not dry out. For chicken thighs the cooking time total is around 10 minutes (I use a Weber charcoal grill), but your grill will be different so rely on your thermometer. The chicken should be very well browned and charred in a few spots.
Oven method: Put in a baking dish ensuring the meat is one layer with the skin side (where the skin was) up. Bake in a 400 F oven until done (about 20 minutes) and registers 160 F on a meat thermometer. Oven method does not work too good for chicken breasts.
Let the chicken rest for 10 minutes and slice into ½ inch thick strips. Tuck in pita bread with plenty of Toom (whipped garlic condiment), shredded lettuce, tomatoes and pickles. Adding French fries to the pita wrap is also traditional.