Preheat oven to 450 degrees. Set a large saucepan of water to boil.
On a large rimmed baking sheet, toss together chicken, garlic, lemons, oregano, and 1 teaspoon oil; season with salt and pepper. Roast chicken, skin side up, until golden and cooked through, 25 to 30 minutes.
Meanwhile, generously salt boiling water. Add orzo, and cook until al dente; drain well, and return to saucepan. Add dill and 1 tablespoon oil; season with salt and pepper, and mix gently to combine.
In a large bowl, whisk together vinegar and remaining 2 tablespoons oil; season with salt and pepper. When chicken and orzo are ready, add arugula to bowl; toss to coat. Drizzle chicken with pan juices, and serve with lemon wedges, orzo, and arugula salad.