Prepare the hollandaise sauce first and keep it warm while you make the English muffins, Canadian bacon, and poached eggs. Avoid overheating the sauce, as hollandaise can separate if it gets too hot.
Melt the butter in a large skillet set over medium heat. Add the English muffin halves and toast for about 2 minutes per side, or until golden and lightly crisp. Remove from the skillet and set aside.
Add the Canadian bacon to the same skillet and cook for about 1 minute per side, or until warmed through and lightly golden around the edges. Remove from the skillet and set aside.
Fill a wide pot or deep skillet with about 3 inches of water. Bring to a boil, then reduce the heat so the water is at a gentle simmer. Stir in the vinegar.
Crack each egg into a small bowl or ramekin. Working carefully, slide the eggs into the simmering water one at a time. Cook for 2-4 minutes, depending on how runny or set you like the yolks.
Remove the eggs with a slotted spoon and transfer them to a paper towel-lined plate to drain briefly.
To assemble, place two toasted English muffin halves on each plate. Top each half with Canadian bacon, one poached egg, a pinch of salt, black pepper, and a generous spoonful of warm hollandaise sauce.
Garnish with fresh chives, if desired, and serve immediately.