Cut the onion into 4 pieces and break the carrots and celery ribs into 2 to 3 pieces. Smash the garlic cloves with the side of a knife. Don't bother peeling your vegetables, that precaution won't be necessary.
Sprinkle a little bit of salt, pepper and dried oregano in the chicken's cavity, then stuff it with the onions, about half the carrots, celery and garlic.
Arrange the rest of the carrots, celery and garlic at the bottom of a 7 quart Dutch oven. Place your chicken over those vegetables and then sprinkle it generously with more salt, pepper and dried oregano.
Put the lid on and place your chicken in the oven for 4 to 5 hours, basting it every hour or so, until it's fall-off-the-bone tender and displays a nice golden skin.
Serve without delay.
This method of cooking chicken naturally generates a beautiful, tasty broth. Whatever you do, do not discard that! You can even make more broth by returning the bones and vegetables you had stuffed inside the chicken to the Dutch oven, top all that with water and then put it back in the oven for an additional 5 to 6 hours, then strain.