Combine all marinade ingredients in a large bowl and whisk together.
Add the chicken thighs and coat evenly.
Cover and chill for at least 1 hour and up to 12 hours
Prepare the sauce by adding all sauce ingredients to a small bowl. Mix together and chill until ready to serve.
Adjust the oven rack about 6 inches (15 cm) from the top heat source in your oven, then preheat the broiler.
Line a baking sheet with foil and a wire rack.
Place chicken in single layer on prepared wire rack, with the smooth sides down. Broil until chicken is well browned and registers at least 165˚F (74˚C), about 16-20 minutes. You may need to rotate the sheet pan halfway through if your broiler heats unevenly. Remove and rest the chicken for 5 minutes before handling, and turn off the oven.
While chicken rests, warm your pitas in the still-warm oven for a few minutes.
Slice the chicken into thin strips and transfer to platter.
Serve with sliced cucumbers, tomatoes, pickles, prepared yogurt sauce, and warm pita.