Bring a large pot of salted water to a boil and cook the orzo until al dente, then drain and rinse with cold water to stop the cooking process.
Slice the chicken breasts into bite-sized pieces and season thoroughly with 1 teaspoon of the dried oregano, sea salt, and black pepper.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, about 6-8 minutes.
In a large mixing bowl, whisk together the remaining 2 tablespoons of olive oil, lemon juice, minced garlic, and the remaining teaspoon of oregano to create the dressing.
Dice the cucumber and red onion, and halve the cherry tomatoes into uniform pieces.
Add the cooked orzo, seared chicken, chopped vegetables, kalamata olives, and crumbled feta cheese to the mixing bowl with the dressing.
Toss all ingredients together until well-coated and garnish with freshly chopped parsley before serving.