Preheat oven to 425°F. Lightly coat a dutch oven with nonstick spray.
Add chopped potatoes and carrots to the dutch oven. Cut onion into large chunks. Set aside ¼ of the onion and put the rest into the pot. Sprinkle with a few pinches of salt.
In a small bowl, add the butter. Zest the orange over the butter, reserving the rest of the orange. Strip the leaves from 2 or 3 of the rosemary sprigs, then chop finely to yield 1 tablespoon fresh rosemary. Add rosemary to the butter along with a pinch of salt and mix well until evenly distributed.
Trim neck from chicken and remove giblets (if included). Rinse chicken inside and out and pat dry.
Rub chicken all over with the butter. Season inside and out with salt and pepper.
Quarter the reserved orange and place inside the cavity of the chicken along with the reserved onion and remaining rosemary sprig. Tie the chicken legs together with kitchen twine. Transfer the chicken to the pot, setting breast-side up on top of the vegetables. If desired, tuck under the wings.
Roast for 15 minutes at 425°F, then bring oven down to 375°F. Continue roasting for 1 hour 15 minutes to 1 hour 45 minutes, until internal temperature reaches 165°F with a thermometer inserted in the thickest part of the thigh.
Let chicken rest, tented with foil, for 15 minutes before serving.