In a large sauté pan over medium heat, warm the olive oil. Add the garlic and cook for about 1 minute. Add the wine, bring to a boil and cook until almost evaporated. Add the asparagus, butter and lemon zest, reduce the heat to medium-low and cook until the butter melts. Season with salt and pepper.
Meanwhile, bring a large pot two-thirds full of salted water to a boil over high heat. Add the pasta and cook according to the package instructions. Drain, reserving 1 cup of the cooking water.
Transfer the pasta to a serving bowl. Add the asparagus sauce and chives and toss to coat. Add the reserved cooking water if the pasta seems dry. Pass the cheese at the table.