When Swiss authorities lifted the veil of banking secrecy—under pressure from the European Union to expose tax dodgers—Singapore stepped in, promoting itself to the world's ultrarich as a discreet place to park cash. Now, the Southeast Asian city-state hopes to persuade them to store their high-priced collectibles here, too.

This week, doors opened to the Singapore FreePort, a super-secure, state-of-the-art facility that operates in its own duty-free zone next to Singapore's Changi Airport. The largest such facility in the world, it provides wealthy collectors with tax-free storage, as well as a place to display and sell their art.