There are conflicting theories about the origin of Eggs Benedict, but most trace the dish to New York City in the late 1800s. Hollandaise sauce is much older: It appears in a French cookbook from 1651 and was later known as Sauce Isigny, named for a town in Normandy. The name was changed to hollandaise after World War I, when butter was scarce in France and had to be imported from Holland.
Make the hollandaise sauce: Melt the butter in a small saucepan over medium heat until no longer foamy (but not browned), 6 to 8 minutes. Transfer the clear butter to a liquid measuring cup, leaving the milk solids on the bottom of the pan; discard the solids.
Heat 1 inch of water in a medium saucepan over medium heat until steaming but not simmering. Combine the egg yolks, 1 tablespoon water and 2 teaspoons lemon juice in a medium stainless-steel bowl. Set the bowl on the saucepan (do not let the bowl touch the water). Cook, whisking constantly, until the egg mixture is pale yellow and thickened, 3 to 5 minutes. Check periodically to make sure the water isn’t boiling or the egg yolks might overcook.
Remove the bowl from the saucepan; slowly pour in the melted butter, a drop at a time at first, whisking constantly until thick. Whisk in the remaining 2 teaspoons lemon juice, the cayenne and ¼ teaspoon salt. If the sauce is too thick, whisk in some warm water, 1 tablespoon at a time, to loosen. Return the bowl to the saucepan of water with the heat turned off to keep warm; whisk occasionally.
Make the Eggs Benedict: Fill a large wide pot with 3 inches of water. Heat over medium-high heat until steaming with small bubbles; reduce the heat as needed to maintain a bare simmer. Stir in the vinegar. Crack 4 eggs into individual small bowls or ramekins. Carefully tip the eggs into the water, spacing them as far apart as possible. Cook until the whites are set but the yolks are still runny, 3 to 3½ minutes. Remove the eggs with a slotted spoon and transfer to a plate lined with a kitchen towel. Gently blot the eggs dry and trim off any wispy pieces. Repeat with the remaining 4 eggs.
Melt the butter in a large skillet over medium-high heat. Add the Canadian bacon and cook until lightly browned and warmed through, 1 to 2 minutes per side. Meanwhile, toast the English muffins and spread with butter.
Top each English muffin half with a slice of Canadian bacon and a poached egg. Thin the hollandaise sauce with more warm water, if necessary, and season with salt. Spoon over the poached eggs and sprinkle with chopped chives.