Combine olive oil, lemon juice, minced garlic, oregano, paprika, salt, and pepper in a bowl and coat chicken thighs. Marinate covered in refrigerator for 30 minutes or up to 2 hours.
Mix Greek yogurt, grated and drained cucumber, minced garlic, lemon juice, fresh dill, and salt in a bowl and refrigerate to allow flavors to meld.
Preheat grill or skillet over medium-high heat. Remove chicken from marinade and cook 6-7 minutes per side until cooked through with grill marks.
Let chicken rest for a few minutes, then slice.
In a large bowl, layer cooked rice as the base. Top with sliced grilled chicken, cherry tomatoes, cucumber, red onion, bell pepper, Kalamata olives, and crumbled feta.
Drizzle tzatziki sauce over the bowl and garnish with fresh parsley. Serve immediately.