In a mixing bowl, combine sliced chicken breast, olive oil, oregano, garlic powder, onion powder, paprika, salt, and pepper. Mix well and let marinate for about 30 minutes (or up to overnight in the refrigerator for extra flavor).
While the chicken is marinating, prepare the tzatziki sauce. Drain the grated cucumber using a clean cloth or paper towel to remove excess moisture. In a bowl, mix the Greek yogurt, grated cucumber, minced garlic, fresh dill, lemon juice, and salt. Adjust seasoning as needed and refrigerate until ready to use.
Heat a skillet over medium-high heat. Add the marinated chicken strips to the skillet and cook for 6-8 minutes, stirring occasionally until the chicken is cooked through and lightly browned.
In the last few minutes of cooking the chicken, add the pita bread to another skillet or warm it in the oven for about 5 minutes until soft and heated through.
To assemble, take a warm pita bread, layer some fresh lettuce or arugula, and top with cooked chicken strips, sliced tomatoes, and red onions. Drizzle with tzatziki sauce generously over the top.
Wrap or fold the pita around the filling and serve immediately with extra tzatziki on the side.
Notes
Serve the gyros on a wooden board lined with parchment paper, with a bowl of tzatziki, garnished with fresh dill or mint on the side.