Mix Greek yogurt, olive oil, lemon juice, garlic, oregano, paprika, salt, and pepper in a bowl. Add chicken and coat well. Refrigerate for 30 minutes to allow the flavors to absorb.
Heat a skillet over medium-high heat. Cook chicken pieces for 5–7 minutes per side until golden and the internal temperature reaches 165°F. Rest for 5 minutes before slicing or portioning.
Cook rice, quinoa, or couscous according to package instructions. Chop cucumber, tomatoes, red onion, and herbs while the grains cool.
Combine Greek yogurt, lemon juice, garlic, olive oil, herbs, salt, and pepper. Stir until smooth and creamy.
Divide grains between containers. Add cooked chicken, vegetables, feta cheese, and herbs evenly. Store sauce separately or add before serving.
Seal containers and refrigerate within 2 hours of preparation. Eat refrigerated bowls within 3–4 days for the best quality.