One evening in the summer of 1972, John Chancellor of NBC began his newscast with a rundown of the day’s reports. War, economic turmoil, the growing Watergate scandal — all of that would be dealt with in due course. “But first,” Chancellor said, “Bobby Fischer.”

That clip appears in “Bobby Fischer Against the World,” Liz Garbus’s fascinating new documentary, as a reminder that, for a moment, Fischer was just about the biggest thing in the world. The matches he played against Boris Spassky in Iceland in 1972 were a global media event. A world championship was at stake, and so were cold war bragging rights, as Fischer, a prickly individualist from Brooklyn, took on Mr. Spassky, a product of the great totalitarian Soviet chess machine. Fischer’s tactical brilliance and nerdy charisma inspired an explosion of interest in the game. Chess clubs popped up in schools all over America, and Fischer was added to the roster of sports heroes that children dreamed of emulating.

But his story has a darker, sadder side that has over the years overshadowed Fischer’s remarkable achievements as a player. His behavior before and during the tournament in Iceland was bizarre. He almost did not show up, taking refuge at the New York home of Anthony Saidy, a fellow American grandmaster and a crucial voice in Ms. Garbus’s film. In Reykjavik he arrived late to matches and complained continually about the conditions of play, actions that were seen by some at the time as a form of psychological warfare intended to throw his opponent off guard.

In the retrospect afforded by Ms. Garbus’s chorus of friends, rivals and colleagues, it seems more likely that the turmoil of Fischer’s inner life was spilling out into the quiet and orderly arena of chess. Almost as soon as the duel with Mr. Spassky was over, Fischer disappeared from public view, only to return two decades later as a decidedly unheroic figure. After playing a tournament in Belgrade in the middle of the Balkan war and in defiance of a United States travel ban, he lived in exile in Japan and Iceland, giving increasingly strident voice to a paranoid worldview rife with conspiracy theories and riddled with anti-Semitism. (Fischer himself was of Jewish background.)