In a small bowl, mix olive oil, lemon juice, oregano, garlic powder, cumin, salt, and pepper to make the marinade.
- Place the chicken breasts in a resealable plastic bag or bowl and pour the marinade over the chicken. Let it marinate in the fridge for at least 30 minutes (or up to 2 hours for more flavor).
- Preheat a grill or skillet over medium heat. Cook the chicken for 5-7 minutes per side until fully cooked and golden brown on the outside.
- Once the chicken is cooked, let it rest for a few minutes, then shred it using two forks or chop it into bite-sized pieces.
- While the chicken is cooking, prepare the tzatziki sauce by combining the Greek yogurt, grated cucumber, lemon juice, minced garlic, olive oil, salt, and pepper in a bowl. Stir well and refrigerate until ready to use.
- Warm the pita or flatbreads in a dry skillet or microwave for a few seconds until soft and pliable.
- Assemble the gyros by placing a generous amount of shredded chicken on each pita. Top with cucumber, tomato, and red onion.
- Drizzle with the tzatziki sauce and garnish with fresh parsley.
- Roll up the pita around the fillings, and serve immediately.