Put on a kettle of 5 to 6 cups of water to boil. Place a flameproof skillet on one side of the grill and preheat the grill over medium flame (about 400). (Note, you can add cold water to the pan, but it is quicker to boil the water first.)
When the water boils add it to skillet along with a big pinch of salt and the vinegar. Carefully crack the eggs and add them to the steaming water. Cover the grill and cook until the eggs are done as desired, 7 to 10 minutes.
Transfer the eggs from the skillet with a slotted spoon, blotting with paper towels to remove excess water and placing in a cup or on top of grilled bread or vegetables. Season with salt and pepper.