In a medium bowl, combine 2 tablespoons olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper. Add chicken pieces and toss to coat. Marinate for at least 15 minutes.
While the chicken marinates, rinse the rice under cold water until water runs clear. In a medium saucepan, bring 2 cups water to a boil. Add rice, reduce heat to low, cover, and simmer for 15 minutes or until water is absorbed and rice is tender. Remove from heat and let stand covered for 5 minutes.
Prepare the cucumber-tomato salad by combining diced cucumber, diced tomatoes, chopped red onion, and parsley in a bowl. Season with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Toss gently and set aside.
Make the tzatziki sauce by combining Greek yogurt, grated cucumber (squeeze out excess moisture), minced garlic, lemon juice, chopped dill, salt, and black pepper in a small bowl. Mix well and refrigerate until ready to serve.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add marinated chicken pieces and cook for 6-8 minutes, stirring occasionally, until chicken is cooked through and lightly browned.
To assemble the bowls, divide cooked rice evenly among four bowls. Top each bowl with cooked chicken, cucumber-tomato salad, a generous dollop of tzatziki sauce, and sprinkle with crumbled feta cheese.
Serve immediately and enjoy your Greek Chicken Bowls.