1Combine 2 tbsp olive oil, minced garlic, fresh oregano, juice of half the lemon, salt, and black pepper in a bowl. Add sliced chicken thighs and toss to coat evenly. Let sit at least 15 minutes or up to 4 hours in the fridge.
2Mix greek yogurt, dill, grated cucumber, squeeze of lemon juice, and a pinch of salt in a small bowl. Taste and adjust—this is your tzatziki.
3Heat 1 tbsp olive oil in a large skillet over medium-high heat. Working in batches if needed, cook chicken until golden and cooked through, about 4–5 minutes per side. Transfer to a plate.
4In the same skillet, quickly soften the sliced onion over medium heat, about 3 minutes, stirring occasionally.
5Warm pita bread in the skillet for 15 seconds per side, or wrap in foil and warm in a 350°F oven for 5 minutes.
6Set out the warm pita, cooked chicken, caramelized onions, tomato slices, lettuce, and tzatziki. Let everyone build their own gyro to taste.