Heat oven to 425 degrees F. Use a large roasting or sheet pan. Keep the pan uncovered.
Whisk together olive oil, lemon juice and zest, garlic, oregano, thyme, salt, pepper, and paprika.
Toss potatoes and carrots with one-third of the marinade. Spread in a single layers and roast 20 minutes.
Coat chicken with remaining marinade. Add chicken to the pan and roast uncovered about 25 minutes. Place the larger breasts toward the outside of the pan.
Toss zucchini and peppers with a little olive oil, salt, pepper, and oregano. Add them, plus onion if using, and roast another 15-20 minutes.
Start checking chicken after about 40 minutes of chicken cooking time. Breasts should reach 165 degrees F, thighs and drumsticks are best at 175-185 degrees F. Large breasts may need 50-55 minutes total.
Remove chicken and loosely tent with foil. Rest 10 minutes. Finish with feta, fresh herbs, Kalamata olives, and lemon wedges.