Step #1 Position the rack in the center of the oven & preheat to 400F degrees F.
Step #2 Pat the chicken dry & sprinkle the cavity with salt & pepper.
Step #3 Stuff the cavity with the orange, lemon, & garlic halves.
Step #4 Tie the chicken legs together with kitchen string to help hold its shape.
Step #5 Sprinkle top the chicken with salt & pepper.
Step #6 Place the chicken, breast side up, on the rack in the pan.
Step #7 Roast the chicken for 1 hr, if necessary, basting every once in awhile & adding some chicken broth to the pan, to prevent the pan drippings from burning.
Step #8 Whisk the orange juice, lemon juice, oregano, oil, & sliced garlic in a medium bowl to mix.
Step #9 Brush some of the juice mixture over the chicken, after it has baked 1 hr.
Step #10 Continue roasting the chicken until an instant-read meat thermometer inserted into the innermost part of the thigh registers 170 degrees F, basting every once in awhile with the juice mixture & adding broth to the pan, about 45 mins longer.
Step #11 Transfer the chicken to a platter.
Step #12 Tent with foil wrap while making the sauce (do not clean the pan).
Step #13 Place the same roasting pan over medium-low heat.
Step #14 Whisk in any remaining broth & let simmer until the sauce is reduced to 1 c, stirring often, about 3 mins.
Step #15 Strain into a 2-c glass measuring c & discard the solids.