In a large mixing bowl, combine the Greek yogurt, lemon juice, garlic, parsley, olive oil, oregano, smoked paprika, cumin, coriander, salt, and black pepper.
Add the chicken pieces to the marinade and toss until evenly coated. Cover and refrigerate for 30 minutes.
While the chicken marinates, prepare the tzatziki sauce. Combine the shredded cucumber, Greek yogurt, lemon juice, dill, garlic, salt, and pepper in a bowl. Stir well and refrigerate until needed.
Heat a large skillet over medium-high heat and lightly coat the bottom with olive oil.
Add the marinated chicken in a single layer. Cook for 3–4 minutes without stirring to allow it to brown.
Flip the chicken and continue cooking for another 4–5 minutes, or until fully cooked and golden.
To assemble the Chicken Gyro Bowls, divide the cooked brown rice among serving bowls.
Top each bowl with cooked chicken, cucumber, tomatoes, red onion, Kalamata olives, feta cheese, and a generous spoonful of tzatziki sauce.
Serve immediately and enjoy.