Preheat the oven to 425°.
Rinse and pat the chicken dry. Salt and pepper the inside of the chicken. Place two orange pieces inside the cavity along with the garlic halves. Rub the chicken with olive oil and season with salt and pepper. Place the chicken in a small roasting pan.
In a bowl, season the remaining oranges and the onions with 2 tablespoons olive oil, 1 teaspoon salt, and 1/2 teaspoon of pepper. Pour the mixture around the chicken.
Roast the chicken for about 1 hour 15 minutes, until the juices run clear when you cut between a leg and a thigh or until a thermometer reads 165°.
Remove the chicken and place on a platter, leaving the lemons and onions in the pan. Cover the chicken with aluminum foil, and allow to rest for 10 minutes while you prepare the pan sauce.
For the pan sauce, place the pan on top of the stove over medium-high heat. Add the broth and stir scraping up the brown bits off the bottom of the pan. Sprinkle in the flour, stirring constantly for a minute, until the sauce thickens. Add any juices that collect on the platter under the chicken and taste for seasoning.
Carve the chicken onto the platter and spoon the onions and sauce over it.
NOTE: Lemons would also be perfect in this recipe.