Pound chicken breasts to even 3/4-inch thickness for consistent cooking. In a large bowl, whisk together olive oil, lemon juice, minced garlic, oregano, smoked paprika, salt, and pepper. Add chicken pieces, ensuring every surface is well-coated with marinade. Let marinate at room temperature for 20 minutes minimum, or refrigerate up to 2 days for deeper flavor development.

Rinse rice under cold water until water runs clear to remove excess starch. Bring 3 1/2 cups water and 1 teaspoon salt to boil in medium saucepan. Add rice, reduce heat to low simmer, and cover tightly. Cook for exactly 18 minutes without lifting the lid. Remove from heat and let stand 5 minutes, then fluff with fork and stir in olive oil and fresh dill.

Grate cucumber using large holes of box grater. Place grated cucumber in clean kitchen towel and squeeze firmly to remove as much water as possible - this prevents watery sauce. In a bowl, combine drained cucumber, Greek yogurt, minced garlic, fresh dill, lemon juice, and salt. Mix well and refrigerate until ready to serve.

Heat 1 tablespoon olive oil in large skillet over medium-high heat until shimmering. Remove chicken from marinade, letting excess drip off. Cook chicken 5-6 minutes per side until golden brown crust forms and internal temperature reaches 165°F. Look for clear juices when pierced with knife. Rest chicken 5 minutes before slicing into strips.

While chicken cooks, dice cucumber, tomatoes, and thinly slice red onion. In a large bowl, combine prepared vegetables with Kalamata olives. Whisk together lemon juice, olive oil, salt, and pepper, then toss with vegetables until evenly coated. Let salad sit to allow flavors to meld while finishing other components.

Divide herb rice among 4 serving bowls as the base. Top each bowl with sliced chicken, Greek salad mixture, and generous dollops of tzatziki sauce. Sprinkle crumbled feta cheese over each bowl and garnish with fresh dill sprigs. Serve immediately while chicken and rice are still warm, contrasting beautifully with cool tzatziki and fresh vegetables.