Marinate the chicken: In a bowl, whisk olive oil, lemon juice, vinegar, garlic, oregano, cumin, salt, pepper, and paprika (if using). Add chicken and coat well.
Marinate for 20–30 minutes (or up to 8 hours in the fridge).
Make the tzatziki: Stir yogurt, grated cucumber, lemon, garlic, dill, salt, pepper, and olive oil. Chill until serving so the flavors meld.
Prep the produce: Dice cucumber, halve tomatoes, slice onion, and chop herbs. Pit and slice olives.
Set aside.
Cook the grains: Prepare brown rice or quinoa according to package directions. Fluff and keep warm. For low-carb, steam cauliflower rice with a pinch of salt.
Cook the chicken: Heat a large skillet or grill pan over medium-high.
Add a light drizzle of oil. Cook chicken 5–7 minutes per side, until internal temp reaches 165°F (74°C). Rest 5 minutes, then slice.
Assemble: Divide grains into bowls.
Top with sliced chicken, cucumber, tomatoes, onion, olives, and feta. Add a spoonful of tzatziki, a squeeze of lemon, and sprinkle with parsley or dill.
Adjust to taste: Finish with a small drizzle of olive oil, extra oregano, or an extra pinch of salt and pepper.