Preheat oven to 425°F.
Place the potatoes, carrots and onions in a roasting pan. Drizzle with olive oil and season with salt, pepper and 2 teaspoons of minced fresh rosemary; toss to coat.
Season chicken cavity with salt and pepper.
Stuff chicken cavity with lemon chunks, celery, rosemary sprigs, thyme sprigs, and garlic cloves. It's fine if you can't fit all of these ingredients into your chicken. Just stuff as much in there as you can!
Place chicken in the roasting pan on top of the vegetable mixture.
Tie the legs together with kitchen string and tuck the wings underneath the bird.
Drizzle or brush melted butter over the outside of the chicken. Season liberally all over with salt and pepper.
Roast the chicken for 1 ½ hours, or until the juices run clear when you cut between a leg and thigh and the temperature on a meat thermometer inserted into the thickest part of the thigh reaches 170-175°F. Check the chicken after the first hour, and if the skin starts to get too dark, tent the chicken loosely with foil for the remainder of the roasting time.
Remove the chicken and vegetables to a platter and cover with aluminum foil. Let rest for about 15 minutes before slicing and serving.