Brown Sugar falls into that spellbinding category: Jagger-Richards songs least likely to be covered by Paul McCartney. This is not merely because the Rolling Stones' 1971 single embodies rock at its most primordial, but because the lyrics are intensely controversial, and to many people, offensive. Yes, despite its throbbing, upbeat tempo and exuberant getaway chorus, Brown Sugar is a song about slave owners having their way with nubile young black women. This is not very nice. It is so not very nice that when the Stones scheduled their 2003 trip to China, the heirs of Mao Zedong, that paragon of cultural sensitivity, singled out Brown Sugar as one of four numbers they were forbidden to play. One can only wonder what the commissars would have made of David Bowie's China Girl or George and Ira Gershwin's flamboyantly condescending Porgy and Bess. Whatever the case, nobody in Chicago, Los Angeles or Leeds ever suggested banning Brown Sugar. Well, at least not any white people.

The emotional apex of virtually every Stones concert, Brown Sugar is an unusual song, in that it is has horns and a bridge and is exquisitely crafted but doesn't end up sounding like Steely Dan schlock. It kicks off with a catchy intro that immediately modulates into a completely different riff, gathers steam with Mick Jagger's sassy vocal, careens off into Bobby Keyes' festive saxophone solo and concludes with one of the most beloved sing-along refrains in the history of rock. A hit single off Sticky Fingers, whose controversial cover was designed by Andy Warhol, Brown Sugar captured the Stones at their apogee, when Mick Taylor was driving the band away from Jones' psychedelia and mysticism and back into blues-based rock. After Taylor made the catastrophic decision to leave the band in 1974, and Ronnie Wood replaced him, the Stones never made another great album.

The genesis of Brown Sugar is shrouded in more mystery than the fate of the Mayans. Mick Jagger insists that he wrote the number in "the middle of a desert in Australia" while he was making the film Ned Kelly in 1969. That was the same summer Brian Jones died in circumstances more mysterious than the fate of the Mayans. Jagger asserts that the song, which dealt with "the dual combination of drugs and girls", simply came to him. But because the guitar lines are so complicated, many people have a hard time believing that this is possible, that Richard and Taylor had to be major factors in the gestation process. Rumours have long circulated that the song was originally entitled Brown Pussy, which would have made it even less likely to surface on Ebony, Ivory and Brown Pussy: Paul McCartney Sings the Jagger-Richards Songbook, and would have drawn even more attention to the offensive lyrics. But Jagger insists this was never the case.

Brown Sugar was recorded in Muscle Shoals, Alabama, in 1969, while the band was touring behind Let It Bleed, the record that vaulted the Stones past the Beatles, now on life support, as the marquis act in rock'n'roll. It was the first time the Stones used a horn section; according to drummer Charlie Watts, the group feared that horns might make them sound like a "show band". Watts also cited the use of horns as a tribute to Otis Redding and James Brown, though a song about white slavers raping black women does seem like an unusual way to play tribute to African-Americans.

Brown Sugar was first performed at the fateful, December 6, 1969, concert chronicled in the film Gimme Shelter. This was the event at which a young black man died after a confrontation with several Hell's Angels, who were providing security. The tragedy is generally singled out as the moment the Sixties officially ended, the moment when the Apollonian promise of Woodstock devolved into the Dionysian horrors of Altamont. In light of the fact that the concert was held in the last month of the last year of the decade, the Sixties would officially have ended in a few weeks anyway. But cultural historians and rock critics love this sort of "seismic watershed" signposting.

Due to legal wrangles involving the band's departure to a new label, Brown Sugar was not released until May 1971. By this point, the Sixties were definitely over. The song was a huge hit and has remained one of the handful of numbers the Stones invariably perform during the hit parade that ends their shows; when the Stones traipse off the stage for that three-song set on their little island, the audience is definitely going to hear Brown Sugar.

The rise of the Internet has allowed all sorts of rumours about the song to flourish. One maintains that a bootleg version showcasing Eric Clapton constituted a sort of informal on-the-spot job interview the Stones held to see who was going to replace Brian Jones. Mercifully, Clapton did not pass the test, perhaps because his soulless virtuosity was a turn-off, perhaps because, unlike the scruffy Ronnie Wood, he simply never looked like a Stone. But then again, neither did the svelte, angelic Mick Taylor.

Many people, myself included, do not mind lyrics as long as they do not get in the way of the music. (This is the way many conductors approach opera, exhorting the orchestra to increase the volume to the point where the singers can no longer be heard.) Those of us who share this view sometimes don't even hear the lyrics. Thus, while I was long aware in a kind of general way that Brown Sugar was a song about a white man with an intense, perhaps unwholesome interest in black women, I wasn't aware of the white-slaver overtones until I went online to read the lyrics. No two ways about it: These lyrics are offensive to black women. These lyrics are deeply offensive to black women. Thank God we have rappers to defend their honour.