Bring 3 cups of water to a boil with the vinegar and salt in a small saucepan over high heat.
Crack an egg into a cup and slide the egg gently into the water. Crack another egg into the cup and while the water returns to a boil, slide this egg into the water as well. Repeat with the third egg. When the water returns to a boil, reduce the heat to low and simmer until the eggs are set. Watch carefully and remove the eggs when the yolks are still soft, about 2 to 2 1/2 minutes. (Test by lifting an egg slightly out of the water on a slotted spoon and gently pressing the center with your finger; the yolk should be soft and the white firm.)
Drain on paper towels. Poached eggs can be made ahead and immersed in a bowl of water in the refrigerator. Reheat by immersing briefly in simmering water.
Recipe adapted from Emeril's New New Orleans Cooking, by Emeril Lagasse, published by William Morrow, 1993