To assemble the gyros, place a pita into the center of a square of foil. One pita per piece of foil. Spread 1/4 cup of the tzatziki evenly, keeping 1 inch away from the edges on all 6 pitas.
Place the chicken, onions, tomatoes, and lettuce in a line going down the middle of the pita. Top with feta and olives. Divide all the ingredients equally between the 6 gyros.
Wrap up the gyro by folding both sides of the pita up and over the filling and wrapping the foil tightly around the gyros.