Cook the orzo: Bring a pot of salted water to a boil.
Cook orzo according to package directions until al dente. Drain and rinse briefly with cool water to stop cooking.
Whisk the dressing: In a small bowl, whisk olive oil, lemon zest and juice, red wine vinegar, Dijon, garlic, oregano, salt, and pepper until emulsified.
Toss warm orzo with dressing: Add the drained orzo to a large bowl and pour over about 3/4 of the dressing. Toss to coat while still slightly warm so it absorbs the flavors.
Add the mix-ins: Fold in chickpeas, chicken, tomatoes, cucumber, olives, red onion, and roasted red peppers.
Finish with herbs and feta: Gently mix in parsley, mint, and feta.
Add the remaining dressing if needed. Taste and adjust salt, pepper, or lemon.
Chill or serve: Serve right away at room temperature, or chill for 30–60 minutes to let flavors meld.