China’s baijiu liquor is the most widely consumed spirit in the world, yet most of the Western world has never heard of it.

That fact has baijiu-maker Luzhou Laojiao Co. eyeing the West. The state-owned distillery in Sichuan province has joined with U.S. and European entrepreneurs in a venture called Ming River, seeking to introduce Americans and Europeans to the popular liquor, one bartender at a time.

It...