In a large bowl, whisk together Greek yogurt, garlic, oregano, thyme, cumin, smoked paprika, salt, and pepper. Add the chicken and toss to coat. Cover and refrigerate for at least 30 minutes, or up to 8 hours.
Heat a large skillet over medium-high heat. Remove the chicken from the marinade and cook for 5 to 7 minutes per side, or until fully cooked and lightly charred. Let rest before slicing.
In a medium saucepan, heat olive oil over medium heat. Add garlic and cook for 1 to 2 minutes. Stir in the rice to coat.
Add chicken broth, lemon zest, lemon juice, and salt. Bring to a boil, reduce heat, cover, and simmer for 15 to 20 minutes, until the rice is tender and the liquid is absorbed. Fluff with a fork.
While the rice cooks, grate the cucumber and squeeze out excess liquid with a towel. In a bowl, mix the yogurt, cucumber, garlic, lemon juice, and dill. Season with salt and pepper. Refrigerate until ready to serve.
To assemble the bowls, divide rice between serving bowls. Top with sliced chicken, tomatoes, cucumber, pickled red onion, and olives. Add a spoonful of tzatziki and finish with feta and parsley.