Whisk the Greek yogurt, egg yolk, lemon juice, and Dijon mustard in a small heat-proof bowl.
Place the bowl over a small pot of simmering water, whisking constantly until the sauce is thickened and warm, then season with salt and pepper.
Fill a medium saucepan with water and the white vinegar, bringing it to a very gentle simmer.
Crack each egg into a small ramekin and gently slide them into the simmering water, poaching for about 3 minutes until the whites are opaque but the yolks remain soft.
Split and toast the whole wheat English muffin until golden brown.
In a dry skillet over medium heat, lightly sear the Canadian bacon slices for 1 minute per side.
Place the bacon on the toasted muffin halves, top with the poached eggs, and generously spoon the warm hollandaise over the top.
Garnish with freshly chopped chives and serve immediately.