In a large bowl, combine marinade ingredients and stir well.
In another large bowl or gallon plastic bag, combine chicken thighs and marinade, stirring well to coat. Cover and refrigerate for at least one hour and up to one day.
Preheat oven to 400°F (200°C).
In a medium bowl, combine tzatziki ingredients and stir well. Cover and refrigerate at least 30 minutes.
On a baking sheet or a large cast-iron skillet, use the onion half as a base and position the skewer vertically like a spit. Skewer the chicken thighs individually, rotating each one 90 degrees. Bake for 1.5 to 2 hours, until internal temperature reaches 165°F (75°C). Let cool for 10 minutes.
Carve off slices of chicken to fill a pita. Top with onion slices, tomato slices, and tzatziki sauce.
Enjoy!