Preheat the oven to 425°F (218°C).
Prep the ingredients per the instructions above.
Make the chicken: In a bowl, mix together all the ingredients for the chicken (except for the onion and skewers). Season with salt and pepper. Marinate for 20 minutes. While the chicken is marinating, make tzatziki sauce.
Make tzatziki sauce: Mix all ingredients together in a bowl. Refrigerate until you are ready to serve.
Place the onion on a baking sheet. Stick the skewers into opposite sides of the onion with the pointed ends facing up. Thread the chicken onto the skewers over the onion (layer the chicken strips on tight).
Cook chicken: Cook in the oven to an internal temperature of 160°F (71°C) using a thermometer. Remove from the skewers and slice the chicken into strips. (discard the onion and skewers).
Assemble gyro: Warm the pita on both sides using the grill or griddle pan.
Spread some of the sauce on the pita, add the chicken, tomatoes, onion, and drizzle more sauce. Then roll up.
Serve: Enjoy gyro with pita chips, hummus (drizzle with oil and dust with paprika if desired), and fruit punch.