Pat the chicken dry and season with oregano, salt, and pepper.
Heat the olive oil in a skillet over medium heat. Cook the chicken until no longer pink in the center, about 6-8 minutes per side depending on thickness. Remove, rest for a few minutes, then slice thinly.
Meanwhile, prepare the orzo according to package directions. Drain and rinse under cold water to stop the cooking and cool it down a bit.
In a large bowl, combine the cooled orzo, cucumber, cherry tomatoes, red onion, olives, and parsley.
Whisk together the lemon juice, olive oil, and garlic (if using). Season with a pinch of salt and pepper.
Add the sliced chicken to the bowl, pour over the dressing, and toss gently to coat.
Crumble feta over the top. Give everything one last light toss and serve, or refrigerate for up to a day to let the flavors meld.