Bring a pot of salted water to boil. Add the orzo, and cook according to package directions. Drain and let cool slightly.
In a large bowl, combine the chickpeas, cucumber, tomatoes, bell pepper, onion, olives, and feta cheese.
Add the cooled orzo, tossing to combine.
In a small bowl, whisk the lemon juice, lemon zest, red wine vinegar, garlic, oregano, and salt together. Slowly add the olive oil, and whisk to combine. Pour over the orzo salad.