In a medium bowl, whisk together olive oil, lemon juice, minced garlic, oregano, thyme, salt, and pepper. Add chicken cubes and toss to coat. Cover and refrigerate for at least 30 minutes (or ideally overnight).
Rinse your rice until the water runs clear. In a medium saucepan over medium heat, heat olive oil. Add rice and cook while stirring constantly for about 1–2 minutes until slightly toasted. Then pour in chicken broth and lemon juice. Bring this mixture to a boil before reducing heat to low. Cover and let it simmer for about 18–20 minutes until cooked through. Stir in parsley and dill while seasoning with salt and pepper.
Grate your cucumber thoroughly then squeeze out any excess liquid. In a medium bowl combine Greek yogurt with squeezed cucumber, minced garlic, lemon juice, olive oil, and dill. Season with salt and pepper before covering to chill in the fridge for at least half an hour.
Preheat your grill to medium-high heat. Thread marinated chicken onto skewers if grilling; otherwise preheat your oven to bake at around 400°F (200°C). Grill each side for about 8–10 minutes until cooked through (internal temperature should reach at least 165°F). If baking, spread evenly in one layer cooking for about 15–20 minutes until golden brown.
Divide your fluffy lemon-herb rice among serving bowls then top generously with grilled chicken pieces, halved cherry tomatoes, cucumber slices, red onion rings, and Kalamata olives. Spoon tzatziki sauce over everything before sprinkling crumbled feta cheese on top along with some fresh parsley. Serve with warmed pita bread or naan if desired.