To make the rice, in a medium saucepan, combine the rice, oil (or butter), oregano, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Add 2 cups of water and set the pan over high heat. Bring to a boil, reduce the heat to low, cover and cook for 15 to 20 minutes, until the liquid is absorbed, and the rice is tender. Fold in the lemon zest and fluff with a fork.
Meanwhile, to make the dressing, combine all ingredients in a medium bowl and mix well. Season to taste with salt and black pepper.
To assemble the bowls, spoon the rice into shallow bowls and top with the chicken, tomatoes, olives, and red onion. Sprinkle the feta cheese over top. Garnish with lemon wedges and serve with the dressing on the side.