Fill a 3-quart saucepan with 2 inches of water and bring to a boil. Boil the asparagus until crisp-tender, 3 to 4 minutes. With a slotted spoon or tongs, transfer to a paper-towel-lined plate.

Add the vinegar to the water, and bring to a simmer. One at a time, crack the eggs into a small bowl and gently slide each egg into the water. Poach until the whites are set, 2 to 3 minutes. With a slotted spoon, remove the eggs from the water in the order they were added and gently blot dry with a paper towel.

In an 8-inch skillet, combine the wine, lemon juice, and shallot. Bring to a simmer over medium-high heat and cook until the liquid has reduced to about 1 Tbs. Turn the heat to low and whisk in the butter a few pieces at a time. It should melt gradually to form a creamy sauce. Stir in the chives. Season to taste with salt and pepper. Top the English muffins with the asparagus, eggs, and sauce. Pass any remaining at the table.