Preheat oven to 375° F.

Cut 1 tangerine in half and set aside. Remove zest from 1 of the remaining tangerines and juice all 3.

Pat chicken dry. Brush skin lightly with olive oil and sprinkle with rosemary, salt and pepper. Stuff the cavity with the halved tangerine and rosemary sprigs.

Scatter onions in a roasting pan and place chicken on top. Roast for 18 to 20 minutes for per pound of chicken (about 1 hour and 15 minutes for a 4-pound chicken). Take the temperature of chicken with a thermometer by placing the thermometer in the meat of the inner thigh, not touching the bone. When the temperature reaches 165° F, remove it from the oven.

Carefully lift chicken from the pan, pouring juices from the cavity into the roasting pan. Place chicken onto a carving board and tent loosely with foil. With a wooden spoon or wire whip, scrape up all of the caramelized bits from the roasting pan, stirring them into the pan juices.

Strain pan juices into a container to allow the fat to float to the top; remove fat. Pour remaining sauce into a wide sauté pan. Add tangerine juice and zest, chicken broth and honey and bring to a boil. Cook, stirring occasionally, until sauce is reduced by half. Adjust the seasoning with salt and pepper.

Carve chicken and serve with tangerine sauce.