Cut potatoes in half, widthwise if your potatoes allow that, thus creating longer but thinner potato halves.
Add cut potatoes to a mixing bowl and add balsamic vinegar, lemon juice, dill weed, chives, salt and pepper. Mix well and spread evenly in a bowl. Cover with Glad Press'n Seal wrap and let it marinate for about 20 minutes.
Once the charcoals are ashed over on the outside, arrange them on half of the grill.
Lay potatoes, cut side down, on the cooler half of the grill. You can spoon some of the herbs and vinegar mixture over each potato. Close the lid on the grill and let potatoes cook for about 10 minutes.
Carefully open the lid and flip each potato. Close the lid and let the potatoes cook for another 10 minutes.
Pick the thickest potato and slide a small knife in the center. If it slides in easily, potatoes are done. If not, they might need a few more minutes.
If you like potatoes to have a bigger crisp to them, slide them over to the hot side of the grill and let them crisp up there for a couple of minutes.