A vast global game of geopolitical chess seemed to be hanging in the balance the morning I met with Garry Kasparov, the Russian chess genius whom many regard as the greatest player of all time.

What’s less well known about him is that for the past decade Kasparov has become a major player in that great game of liberty versus tyranny in which the globe is the board. He was jailed and, as recently as 2012, beaten in Moscow for protesting Vladimir Putin’s regime and its crackdown on civil liberties, and he’s been driven out of his homeland. After daring a presidential election challenge to Putin in 2007, one that was disqualified under murky circumstances, and a number of what he calls “accidents,” he no longer feels life and liberty are safe there.

Not that his life is necessarily safer anywhere else in the world, as the fate of Russian dissident Alexander Litvinenko—who was poisoned with polonium-laced tea in a posh London hotel in 2006—attests.

No tea was served in the mazelike reception lounge area of the large Upper West Side apartment complex where we met. Kasparov, 50, came barreling out of the elevator, a compact fellow with the physique and the no-nonsense mien of a welterweight boxer. He had just returned from the World Chess Championship in India where his former protégé Magnus Carlsen, a then 22-year-old Norwegian prodigy, stunned the world with a smashing victory over the reigning champion, Viswanathan Anand.

Kasparov, who became the 13th world champion in 1985 and was ranked number one in the world until he retired in 2005, seems genuinely in awe of Carlsen’s ability: “He has unique chess talents,” says Kasparov, who trained Carlsen for a year back in 2009. “I would say that he is a combination of Bobby Fischer and Anatoly Karpov [the Russian world champion whom Kasparov dethroned]. Because he has Karpov’s precision and ability to just locate the piece’s best positions but also Fischer’s determination. So he can play to the last point, the last moment, last chance, and some people say he’s good at squeezing water out of stone.” Meaning he can see possibilities of victory even in often bleak-looking end-game boards, possibilities that can be obtained only by exploiting minute, nearly invisible positional advantages. In fact, Kasparov believes the Norwegian has so far-outdistanced the rest of the world that he will not be beaten by anyone “for next five years, at least,” although Kasparov thinks an American, Hikaru Nakamura, he had been bringing along may have a chance.

Invisible positional advantages are what Kasparov must hope for in the global human rights game he’s playing now. His chief opponent, Putin, has a nuclear arsenal and a much-feared army of intelligence operatives, the FSB, as the successor organization to the KGB is called today. Kasparov’s “invisible” arsenal is moral force, which sometimes—as the recent celebration of Nelson Mandela reminds us—can triumph after years of struggle. But the odds are heavily stacked against him.

Kasparov speaks with a kind of Russian stoicism about his entry into politics: “I was not playing to win, it was just something I believed was important for me as a human being. So it’s like a moral imperative rather than coldblooded calculation.”

Kasparov is now chairman of the international council of the Human Rights Foundation, an organization identified with Vaclav Havel, one of modern history’s greatest dissidents, whose Velvet Revolution in Czechoslovakia was a landmark in the beginning of the end of the Soviet empire—but not the end of repression in Russia. After a coterie of Harvard-based economic advisers helped engineer the privatizing of Russian state assets in the 1990s to the profit of corrupt oligarchs, the consequent immiseration of the Russian people led to Putin’s rise to power. And that led to Putin’s ongoing attempt to recoup what had been lost—seeking to recapture the states that had separated themselves from the Soviet empire, and to crush democracy within Russia.

This very morning it looked as if Putin had pulled off another bold move, what might be called in chess terms, “Putin’s Gambit,” his attempt to recapture Ukraine, the lost queen of the new Russian empire, from the seductive embrace of the West.

I show Kasparov the morning’s Wall Street Journal dramatic Page 1 headline: “Ukraine’s Pivot to Moscow Leaves West out in the Cold.” The gist: When it looked as if Ukraine President Viktor Yanukovych was about to sign long-negotiated economic agreements that would bring it closer to membership in the European Union, he was reportedly summoned for a chat with Putin and, not long afterward, announced that he had decided not to sign the agreements. It was widely reported that Putin had used a combination of threats, bribes and economic enticements to lure Ukraine back.

As Kasparov and I spoke in New York, halfway across the globe in Kiev, Ukraine’s capital, tens of thousands were converging to protest what they regarded as their being sold back into neo-Soviet satellite status, toppling the statue of Lenin in Kiev’s main square. As I write, there are despairing reports of heavily armed police storming into opposition TV and radio stations. By press time, the violence was intensifying and spreading throughout Ukraine, no endgame in sight.

Foreign policy commentators were speaking of this as a decisive moment in post-cold war history. And Garry Kasparov, I came to realize, as he analyzed the news, was viewing the episode in the perspective of the history not just of the past two decades, but of the past century. He sees the contemporary situation as a badly played chess match in which the West lost its chance to press its advantage after the fall of the Soviet Union, instead complacently settling for what looked like a draw—one that now might turn into a decisive loss.

What impressed me about Kasparov was how well read and sophisticated in his knowledge of history and international politics he was. Chess genius does not always translate to real-world intelligence (Bobby Fischer ended up as a paranoid Holocaust denier). And Kasparov deplores the tragic depiction of a Russian prodigy in Nabokov’s chess novel, The Defense.

He’s deeply learned in history and historical parallels. When the talk turns to the Sochi Olympics, he refers back to the German games of 1936: “The Olympics started four months after Germany [remilitarized the Rhineland], violating Versailles agreement, and within one month after the beginning of the civil war in Spain. Soon German planes were bombing Spanish cities—the Western powers pretended it was business as usual.”

“You think the Sochi Olympics is...?

“The Sochi Olympics, I think, might be a total disaster, [but] we’re lucky. Because [the difference between] Hitler and Putin is that Putin doesn’t have a proper organization behind him in Russia.”

Kasparov’s animus toward Putin led me to ask the philosophical question “Do you believe in evil?”

“Everyone has an evil component within,” he tells me. “It’s matter of circumstance whether it emerges. Whether he becomes ‘the right man in the right place at the right time’ for evil to emerge. Stalin had it, all the components in place.”