In a large bowl, or gallon-sized plastic zipper bag, add chicken breast pieces, olive oil, lemon juice, oregano, garlic, salt, and pepper. Cover, refrigerate, and let marinate for at least 1 hour or over night.
When you are ready to cook the chicken, remove from marinade and place on a grill ban or rack. Broil in oven, or grill for 5 minutes on each side.
For the Rice:
Heat olive oil over medium heat in a medium size saucepan. Add onion and saute until translucent, about 5 minutes.
Add rice and stock and bring to a boil. Once it comes to a boil, reduce the heat, stir the rice, cover, and let simmer according to package cooking time.
For the Tzatziki
Place the grated cucumber in a fine mesh strainer over a bowl. Sprinkle with salt and let sit for 10 minutes. After 10 minutes, squeeze and drain as much water as you can out of the cucumber.
In a medium bowl, combine the yogurt, drained cucumber, vinegar, garlic, dill, salt, and pepper. Cover and refrigerate until ready to use.
For the Salad:
In a medium bowl, combine cucumber, tomatoes, onion slices, olive oil, oregano, salt and pepper. Toss and serve.To assemble the dish, place rice into a bowl. Top with a piece of chicken, a scoop of tzatziki, and some salad. Enjoy!