In a gallon size Ziploc bag, combine chicken, 1/4 cup olive oil, garlic, lemon juice, red wine vinegar and oregano; season with salt and pepper, to taste. Marinate for at least 20 minutes to 1 hour, turning the bag occasionally. Drain the chicken from the marinade, discarding the marinade.
Heat 2 tablespoons olive oil in a large skillet over medium high heat. Add chicken to the skillet and cook, flipping once, until cooked through, about 3-4 minutes per side. Let cool before dicing into bite-size pieces.
To make the cucumber salad, combine cucumbers, onion, lemon juice, olive oil, red wine vinegar, garlic and oregano in a small bowl; set aside.
To make the tzatziki sauce, combine Greek yogurt, cucumber, garlic, dill, lemon juice, lemon zest and mint in a small bowl; season with salt and pepper, to taste. Drizzle with olive oil. Refrigerate for at least 10 minutes, allowing the flavors to meld; set aside.
In a large saucepan of 2 cups water, cook rice according to package instructions; set aside.
Divide rice into meal prep containers. Top with chicken, cucumber salad, tomatoes and tzatziki sauce.