Heat the oven to 400°F and grease a 9-by-13-inch baking dish.
Toss the chicken with the olive oil, oregano, salt, pepper and lemon zest directly in the dish.
Stir in the orzo, broth, garlic and lemon juice and spread the chicken pieces into one even layer.
Cover tightly with foil and bake for 20 minutes.
Uncover, stir in the spinach and bake for 10 to 15 minutes more, until the orzo is tender and every chicken piece reaches 165°F.
Rest for 5 minutes and stir once more so the remaining broth coats the orzo.