Driven by a popular urge to defeat corruption in recent years, Russian President Vladimir Putin has been a man on a mission. He cracked down on media mogul Vladimir Gusinsky for alleged embezzlement. Putin is trying to extradite tycoon Boris Berezovsky, who resides in exile in London, on criminal fraud charges. The Russian president’s most notable crusade has been against the giant oil company Yukos, which was run by billionaire Mikhail Khodorkovsky. The government effectively confiscated Yukos in late 2004. Its former CEO was convicted of fraud and tax evasion in a kangaroo court and is currently serving an eight-year sentence in a Siberian labor camp.

Khodorkovsky is the most prominent member of the new oligarchs, the class of Russian businessmen who amassed great wealth and power after the collapse of the Soviet Union. In the mid-1990s, the government auctioned off key state assets to well-connected entrepreneurs. These young capitalists took on the challenge of transforming seemingly moribund Soviet smokestacks into beacons of industry. Businesses were able to grow by taking advantage of a weak legal system that failed to defend property rights and enforce contracts. Soon enough, the new magnates succeeded beyond all expectations, amassing fortunes that ran into the billions of dollars. And, because they had little faith in the Russian legal system’s ability to protect their property, the new entrepreneurs took out their own version of an insurance policy—paying off politicians, judges, and other officials.

The rise of these oligarchs puts Russia in a dilemma. The government needs to safeguard the generators of the country’s unprecedented economic boom. Russia’s gross domestic product has expanded by an average of 7 percent a year since 1999, and oligarch-owned oil companies have increased their production even faster. At...