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 ask -- if you can get it.

For the 26 monks at St. Sixtus, however, success has brought a spiritual hangover as they fight to keep an insatiable market in tune with their life of contemplation.

The monks are doing their best to resist getting bigger. They don't advertise and don't put labels on their bottles. They haven't increased production since 1946. They sell only from their front gate. You have to make an appointment and there's a limit: two, 24-bottle cases a month. Because scarcity has created a high-priced gray market online, the monks search the net for resellers and try to get them to stop.

"We sell beer to live, and not vice versa," says Brother Joris, the white-robed brewery director. Beer lovers, however, seem to live for Westvleteren.