IN 1958, Sherman Adams, President Dwight Eisenhower's forceful chief of staff, was one of Washington's most influential men. His career, however, ended abruptly after he accepted an overcoat from a textile magnate under federal investigation. The gift might seem innocuous enough, but the coat in question was made of vicuña—an incredibly soft, light, rare and very expensive yarn. It was alleged that Mr. Adams, swayed by such luxurious gifts, subsequently tried to influence federal agencies on the magnate's behalf. Despite the politico's protestations of innocence, he resigned in a scandal that some dubbed the Vicuña Coat Affair.

If Mr. Adams were indeed guilty, he would not have been the first to fall under the spell of vicuña. Incan royalty wore it exclusively. In the 1500s, King Philip II of Spain slept under vicuña blankets. Last century, it was favored by wealthy entertainers: Greta Garbo wore vicuña, as did Nat King Cole and Marlene Dietrich.

Now, the silky wool sits at the nose-bleed-high pinnacle of tailored luxury. Each year, only 13,000 to 17,500 pounds of vicuña become available to Loro Piana, a major purveyor of vicuña garments—a fraction of the 22 million pounds of cashmere the company works with annually. The Italian tailoring house Kiton makes only about 100 vicuña pieces a year; an off-the-rack sport coat costs at least $21,000, while the price of a made-to-measure suit starts at $40,000. A single vicuña scarf from Loro Piana is about $4,000. Ermenegildo Zegna produces just 30 vicuña suits a year. Each is numbered, and the most affordable model goes for $46,500.

Not long ago, however, vicuña was even harder to come by. The vicuña, a camelid that looks like a smaller and more elegant llama, is found primarily in the Peruvian and northern Argentine Andes. For centuries, it was poached for its valuable cinnamon-colored coat, a marvel of evolution that, although unusually light and fine, keeps the animals warm in the freezing altitudes above 15,000 feet. By the 1960s, the vicuña population had fallen from an estimated two million in the 16th century to roughly 10,000, and Peru took measures to protect vicuñas from extinction, banning the killing and trade of the animals.

But in the mid-90s, companies eager to provide the uber-luxurious fiber to their customers began working hard to find a way to preserve the animals' population and to shear their hair, instead of killing them. In 1994, three companies—Loro Piana, Agnona and Incalpaca TPX—were selected to join an International Vicuña Consortium created by the Peruvian government, earning the right to humanely process and export vicuña fiber as fabrics and finished products.