1) For the hollandaise sauce: In a medium pan, completely melt the butter over medium-low heat. Remove from the heat and set it aside for 5 minutes. Skim and discard the white foam that rises to the surface of the butter. Carefully ladle or pour the clear golden butter into a container with a pouring spout. Take care not to add the milky solids and watery liquid at the bottom of the saucepan. Set the butter aside in a warm spot.
2) Pour enough water into a medium saucepan to reach a depth of about 5cm. Bring to a gentle simmer over medium heat.
3) In a medium heatproof bowl, combine the egg yolks and the cold water. Whisk until the yolks are light and frothy. Place the bowl over the saucepan of simmering water and whisk constantly and vigorously until the yolks are thickened and light, about 3 to 4 minutes. (If the eggs begin to scramble, or the mixture is cooking very quickly or gets too hot, remove the bowl from the heat and whisk to cool). Remove the eggs from the heat and whisk for 30 seconds to cool slightly.
4) Remove the saucepan from the heat and set the bowl over the hot water. Slowly drizzle the butter into the eggs while whisking constantly. Whisk in the lemon juice, salt, and pepper, to taste. (If the sauce is very thick, add a few drops of warm water to adjust the consistency so it is creamy and light.) Serve immediately or keep the hollandaise sauce in a small bowl set over warm, but not hot water, for about 30 minutes or in a warmed thermos for about an hour.
5) For the eggs: Pour enough water into 2 large skillets to reach a depth of about 8cm, and divide the vinegar between them. Bring both skillets to a gentle simmer over medium heat. Crack an egg into a cup and carefully slide it into the hot poaching liquid. Quickly repeat with all the eggs. Poach the eggs, turning them occasionally with a spoon, until the whites are firm, or to the desired degree of doneness, about 3 to 5 minutes. Using a slotted spoon, remove the eggs and transfer to a kitchen towel. Lightly dab the eggs with the towel to remove any excess water.
2) While the eggs are poaching, melt the butter in a large skillet over medium heat. Add the bacon and cook until heated through, about a minute on each side.
3) To serve, toast the English muffin halves and divide them among 6 warmed plates. Top each half with a slice of Canadian bacon, and set an egg on top. Spoon the hollandaise sauce over the eggs and garnish with the chives. Serve immediately.