Fill large stockpot with at least four inches of water. Bring to a rolling boil. Add vinegar and cover. Reduce heat so that the water stays as hot as possible without maintaining a boil.
Crack one egg into a tea cup. Gently pour the egg into the water from the cup, holding as close to the water's surface as possible.
Repeat with as many eggs as you feel comfortable cooking at the same time, ensuring there is enough room such that the eggs don't touch. Cover.
After at least 30 seconds has passed to ensure the egg has partially cooked, release any eggs that may be sticking to the bottom of the pot by gently easing a spatula underneath.
To check doneness, use a slotted spoon to lift the egg to the water's surface. Remove from water when white appears firm but yolk is still jiggly.