Prep the ingredients per the instructions above.
Make the chicken: In a bowl, mix together all the ingredients for the chicken. Season with salt and pepper. Marinate for 20 minutes. While the chicken is marinating, make tzatziki sauce.
Make tzatziki sauce: Place all ingredients in a blender; blend until smooth. Taste and add more seasoning (lemon juice, salt, pepper) if needed. Refrigerate until you are ready to serve.
Heat a grill or griddle pan on medium heat.
Cook chicken: Remove chicken from the marinade, letting any excess sauce drip off. Grill chicken for about 6 minutes on each side, flipping once until cooked through to an internal temperature of 160 °F (70 °C) using a thermometer. Remove to a plate to rest before chopping into bite-size pieces.
Assemble gyro: Warm the pita on both sides using the grill or griddle pan. Layer with lettuce, chicken, red onion, grape tomatoes, olives, feta, and sauce.
Serve: Enjoy gyro with pita chips, hummus (drizzle with oil and dust with paprika if desired), and cola over ice.