Prepare a gas or charcoal grill for rotisserie cooking over indirect medium heat (or according to the instructions for your grill). Place the drip pan under the center of the spit.
In a small saucepan, combine the marmalade, orange juice, balsamic vinegar, garlic, and rosemary and bring to a boil. Reduce the heat to medium-low and gently simmer for 5 minutes. Remove from the heat and let cool. Pour 1/4 cup of the sauce into a small bowl to use for basting the duck, and pour the rest into a small serving bowl for passing at the table.
Meanwhile, remove all the excess fat from the duck. Wash the duck and dry it thoroughly both inside and out with paper towels. With a sharp metal skewer, prick the duck skin all over, especially the thighs, 50 times. Season the duck inside and out with salt and pepper to taste. Tie the legs together and brush the duck all over with a light coating of the orange-marmalade mixture.
Place the duck on the spit and secure it with the clamps. Attach it to the rotisserie mechanism, cover the grill, and cook until the temperature in the thickest part of the thigh reaches 160°F (71°C), 1 1/4 to 1 3/4 hours, depending on the heat of your grill. About 15 minutes before the duck is done, brush it all over again with more of the orange sauce. When the duck is done, transfer it to a cutting board and let rest for 15 minutes.
Carve the duck and pass the remaining orange sauce on the side.