Rinse the rice under cold water until the water runs clear.
In a medium saucepan, combine the rice and 2 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to low, cover, and simmer for 15 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 marinade for the chicken by combining 2 tablespoons olive oil, 2 tablespoons lemon juice, 3 minced garlic cloves, dried oregano, ground cumin, salt, and black pepper in a bowl.
Add the chicken breasts to the marinade, coating them evenly. Let marinate for at least 15 minutes.
Preheat a grill pan or skillet over medium-high heat.
Grill the marinated chicken breasts for 6-7 minutes per side or until fully cooked and internal temperature reaches 165°F (74°C). Remove from heat and let rest for 5 minutes.
While the chicken rests, prepare the tzatziki sauce by mixing Greek yogurt, chopped fresh dill, 1 tablespoon lemon juice, 1 minced garlic clove, salt, and black pepper in a small bowl. Stir until smooth and refrigerate until serving.
Slice the grilled chicken into strips.
Assemble the bowls by dividing the cooked rice evenly among four bowls.
Top each bowl with sliced chicken, cherry tomatoes, diced cucumber, sliced red onion, Kalamata olives, and crumbled feta cheese.
Drizzle each bowl with tzatziki sauce before serving.