Greek chicken gyros have herb and spice marinated chicken that is layered with fresh sliced tomatoes and red onions and tucked into a pita with a dollop of homemade tzatziki sauce.
Combine olive oil, oregano, thyme, cumin, red pepper flakes, salt, and sesame seeds in a medium bowl. Stir to combine. Add chicken and toss to coat. Cover bowl with plastic wrap or foil and place into refrigerator for 30 minutes to marinate. Meanwhile, make the tzatziki sauce.
Place tzatziki ingredients into a food processor and processes for 1 minute. Refrigerate until ready to use.
Heat 2 tbsp olive oil in a skillet over medium heat. Carefully place chicken into the hot pan, making sure you don't overcrowd the pan. Depending on the size of your pan, you may need to do this in 2 separate batches. Add additional oil as needed in between batches. Cook chicken until cooked through, 4 to 5 minutes per side.
Assemble the gyros starting with the pita bread, cooked chicken, 3-4 slices of tomatoes, a few strings of onions, and last, tzatziki. Repeat with remaining ingredients and serve.