Preheat oven to 350ᵒ. Place the onion and olive oil in a small ovenproof pan and cover tightly. Roast for 50 to 60 minutes, or until the onion is soft. Let the onion cool in the olive oil, and then remove the onion, reserve the oil. Julienne the onion and place in a medium bowl.
Add the balsamic vinegar and slowly whisk in the reserved olive oil. Add the chives and season to taste with salt and pepper.
Prepare the broiler. Rub the beef with the olive oil and season to taste with salt and pepper. Broil for 4 to 5 minutes on each side, or until to desired doneness. Remove the beef from the oven and let rest for 5 minutes. Cut into ¼ inch thick slices.
Bring a medium pot of salted water to a boil. Add the asparagus and cook for 5 minutes, or until tender. Fan the asparagus on each plate, layer the beef slices in an overlapping pattern over the asparagus and spoon the vinaigrette over.