Place the grated cucumber in a kitchen towel and wring out as much water as you can. This prevents the sauce from getting watery.
Add the squeezed cucumber to a bowl, along with the rest of the ingredients. Cover and refrigerate for at least 30 minutes.
For the chicken souvlaki
In a medium bowl, combine the olive oil, lemon juice, minced garlic, oregano, paprika, salt, and black pepper. Add the chicken and coat them thoroughly. Cover and marinate in the refrigerator for at least 30 minutes.
Heat a grill pan over medium-high heat. Coat the pan with oil, then cook the chicken for 3-4 minutes on each side, or until the center reaches 155°F. Remove to a plate.
For the bowls
Divide the cooked rice into four bowls. Top each with the cooked chicken, shredded lettuce, cherry tomatoes, cucumber, red onion, olives, and feta cheese.
Drizzle on the tzatziki sauce and optionally serve with some fresh pita. Enjoy!