WESTVLETEREN, Belgium -- The Trappist monks at St. Sixtus monastery have taken vows against riches, sex and eating red meat. They speak only when necessary. But you can call them on their beer phone.

Monks have been brewing Westvleteren beer at this remote spot near the French border since 1839. Their brew, offered in strengths up to 10.2% alcohol by volume, is among the most highly prized in the world. In bars from Brussels to Boston, and online, it sells for more than $15 for an 11-ounce bottle -- 10 times what the monks...