In a medium saucepan, bring 2 cups of water to a boil. Add the rice, reduce heat to low, cover, and simmer for 18 minutes or until the rice is tender and water is absorbed. Remove from heat and let it sit covered for 5 minutes.
While the rice cooks, prepare the chicken. In a medium bowl, combine 1 tablespoon olive oil, dried oregano, garlic powder, salt, and black pepper. Add the chicken pieces and toss to coat evenly.
Heat the remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chicken and cook for 6-8 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove from heat.
In a small bowl, make the tzatziki sauce by combining Greek yogurt, lemon juice, fresh dill, minced garlic, and a pinch of salt and pepper. Mix well and refrigerate until ready to serve.
To assemble the bowls, divide the cooked rice evenly among four bowls. Top each with cooked chicken, diced cucumber, cherry tomatoes, Kalamata olives, red onion, and crumbled feta cheese.
Drizzle each bowl with the tzatziki sauce. Serve immediately.