In a medium mixing bowl whisk together orange marmalade, olive oil, Worcestershire sauce, fresh orange juice, fresh lemon juice, dried thyme, dried oregano, salt, and black pepper until smooth.
Stir in the thinly sliced shallot to the marinade, then set the mixture aside.
Place the cleaned chicken halves in a deep dish and pour about half the marinade over them, using a pastry brush to coat all sides.
Cover the dish with plastic wrap and refrigerate for at least 2 hours, turning the chicken once to marinate both sides.
Preheat the oven to 375°F (190°C).
Lightly spray a large baking sheet or roasting pan with nonstick spray or line it with parchment paper, then arrange the orange and lemon slices in a single layer on the sheet.
Transfer the chicken halves to the prepared baking sheet, resting them on top of the citrus slices, and pour the remaining marinade over the chicken.
Bake for 45 to 55 minutes, basting with pan juices every 15 minutes, until a meat thermometer inserted into the thigh reads 165°F (74°C) and juices run clear.
Remove the chicken from the oven and let it rest for 10 minutes before carving and serving.