Take the chicken breast out of the refrigerator approximately 30 minutes before poaching.
Put the 4 quarts of water in a large pot that has an accompanying lid. A six-quart pot or a stock pot will work well. Bring to a rapid boil.
Add the chicken breasts to the water and then wait until the water comes back to a rolling, vigorous boil. Put the lid on the pot, turn off the heat and remove pot from the hot burner. Do nothing to the pot, do not remove the lid or sneak a peek in the pot for one hour.
When the hour is up, remove the chicken breasts and put them in a colander over a bowl. Do not throw away the poaching liquid. Freeze it for future poaching or use in soups. I personally add a bay leaf, peppercorns and a pinch of salt to the poaching liquid before I add the chicken.
Let the breasts cool down and then put them in a container or covered bowl to chill. The chicken will slice more evenly once chilled.
Freeze any unused poached chicken for future use.