Rinse and cook the rice according to package directions. Fluff and keep warm.
Preheat oven to 400°F (200°C). Coat chicken with 1 tbsp olive oil, oregano, lemon juice, salt, and pepper. Roast 20–25 min, rest 5 min, then slice.
Stir store-bought hummus or blend your own with chickpeas, tahini, lemon, garlic, and olive oil.
Make the salad. Toss tomatoes, cucumber, onion, and olives with 1 tbsp olive oil, lemon juice, salt, and pepper.
Layer rice, chicken, hummus, and salad in bowls. Top with feta and an extra drizzle of olive oil.