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Step 1
Preheat the oven to 425 degrees F (220 degrees C). Set a roasting rack inside a rimmed baking sheet. Pat chicken dry with paper towels.
Step 2
Zest 1 teaspoon lemon zest into a small bowl. Quarter remaining lemon and place pieces inside chicken cavity along with onion and garlic.
Step 3
Add mayonnaise, vinegar, Worcestershire, and cayenne to the lemon zest; mix to combine. Rub mayonnaise mixture evenly all over the chicken and underneath the skin over the breast. Sprinkle chicken evenly with salt and pepper.
Step 4
Roast in the preheated oven until no longer pink at the bone and the juices run clear, 50 to 60 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 165 degrees F (74 degrees C). Tent with foil halfway through cooking if too much browning occurs before internal temperature is reached. Let stand for 10 minutes before serving.