Preheat the oven to 400°. Finely grate the zest of 1 lemon and 1 orange. Quarter the zested lemon and orange.
Set the chicken on a rack in a roasting pan. In a small bowl, combine the citrus zests with 1 tablespoon of the ginger.
Generously season the cavity of the chicken with salt and pepper and all of the zest mixture.
Stuff as many lemon and orange quarters inside the chicken as will fit.
Juice the remaining 2 lemons and 1 orange. In a small bowl, mix the citrus juice with the remaining 2 tablespoons of ginger, the olive oil and the honey.
Brush the chicken with the juice mixture and roast, basting with the juice every 20 minutes, for 1 1/4 hours, or until an instant-read thermometer inserted in the thickest part of a thigh registers 165°.
If the skin browns too quickly, cover the chicken with foil.
Transfer the chicken to a cutting board and let rest for 15 minutes. Pour the pan juices into a glass measuring cup and skim off the fat.
Remove the chicken skin and discard, carve the meat and transfer to plates. Serve with the pan juices.