In a large bowl, combine olive oil, Greek yogurt, lemon juice, minced garlic, dried oregano, cumin, salt, and black pepper. Stir until well blended. Add the diced chicken breasts and coat them evenly with the marinade. Cover and let it sit in the refrigerator for at least 30 minutes, or up to 2 hours for deeper flavor.
In another bowl, mix together the plain Greek yogurt, diced cucumber, fresh lemon juice, minced garlic, and chopped dill. Stir until all ingredients are well combined. Refrigerate until ready to serve.
Heat a skillet or grill pan over medium-high heat. Once hot, add the marinated chicken pieces and cook for about 5-7 minutes, or until golden brown and cooked through. Ensure the chicken reaches an internal temperature of 165°F (75°C).
In a serving bowl, add a generous scoop of cooked brown rice as your base. Top with the cooked chicken, halved cherry tomatoes, sliced red onion, Kalamata olives, and dollops of tzatziki sauce. Finally, finish with crumbled feta cheese for that extra burst of flavor.
Your Gyro Bowl is ready to be served! Enjoy it fresh, or pack it for lunch.