Put the water in a fairly wide nonstick skillet. Add the vinegar and bring to the simmer.
As gently as possible, break the eggs into the water, taking care that they are spaced apart so that the whites do not touch. The water should be barely simmering. Cook until the whites are set and the yolks remain runny, 2½ to 3 minutes. Using a slotted spoon, drain the eggs on paper towels, handling them as carefully as possible to prevent the yolks from breaking.