Remove the chicken from the refrigerator ~20 minutes before roasting.
Preheat oven to 375°F. Position oven rack in lower third of oven.
Remove the leaves from 2 of the rosemary sprigs; finely chop rosemary. (Note: The remaining sprigs of rosemary will be used later.)
Using a small bowl, combine the chopped rosemary, softened butter, minced garlic, lemon zest, salt and pepper.
Pat the chicken dry with paper towels. Carefully pull the skin away from the chicken and rub the butter mixture all over the chicken (both on top of the skin and under the skin).
Stuff the cavity of the chicken with the onions, garlic, lemons and remaining rosemary sprigs. (Note: If some of these ingredients don’t fit, just place them in the Dutch Oven outside of the chicken.)
Using kitchen twine, tie the chicken legs together. Tuck the wings behind the bird to prevent them from burning.
Place chicken in the Dutch Oven breast-side up.
Cover pot and roast the chicken for 60 minutes.
Increase oven temperature to 400°F and remove the lid of the Dutch oven. Continue roasting uncovered for 20-30 minutes, or until the internal temperature is 165°-175°F. (Insert the thermometer into the deepest part of the thigh without touching bone.) See note below.
Remove Dutch Oven from oven and let chicken rest for 15-20 minutes before carving.
Notes
Keep an eye on the chicken during the last uncovered phase. If it is browning too quickly, tent with aluminum foil.