Cut chicken thighs into 1-inch strips and marinate in olive oil, oregano, garlic powder, salt, and pepper for at least 2 hours.
Heat a skillet over medium-high heat and cook chicken strips until golden brown (about 6-8 minutes).
For the tzatziki, grate cucumber, drain moisture, and mix with Greek yogurt, feta cheese, minced garlic, lemon juice, salt, and pepper. Chill for at least 30 minutes.
Prepare toppings by slicing cherry tomatoes and red onion.
Warm pita breads in a skillet or microwave until soft.
Assemble gyros by spreading tzatziki on pita, adding chicken strips and veggies. Fold and enjoy!