Right after Like a Virgin, which he produced for Madonna, and before Lost in Music, the 1979 hit he wrote for Sister Sledge, Nile Rodgers beams out into this adoring Saturday-night crowd. "You know what tonight is like?" he inquires of them. "It is like, 'This is Your Life, Nile Rodgers' – in song!"

It is, and what a life it has been. Rodgers's revival, at 60, in 2013 – two years after surviving aggressive prostate cancer – is due to his guiding presence on Get Lucky, Daft Punk's irresistible million-selling summer hit. It has triggered, too, a welcome rehabilitation of Chic, his 70s disco group who bestrode the pop world like preposterously funky colossi.

There is an old-fashioned look to this show, with Rodgers's nine-piece band all in white – down to their shoes – and two perma-grinning, soulful female singers, but nothing fusty about the music. Whether reprising hits that Rodgers shaped for Diana Ross, Duran Duran and David Bowie, or their own gleaming back catalogue, Chic's grooves pulse with giddy euphoria, a profound joy; an adorable lightness of being.

Rodgers's scratchy, James Brown-indebted guitar is at the heart of all that is good about the band. Fluid and amorphous, it itches like jangling heartstrings on Sheila and B Devotion's 1979 hit Spacer and Chic's colossal Le Freak, the very essence of disco. Playing them both, Rodgers grins like a man who can't quite believe this is all happening. For the encore of Chic's manifesto statement, Good Times, the band are joined on stage by an army of audience members doing the kind of heroically bad dancing that usually happens around handbags. It has the net effect of making the unassuming Nile Rodgers appear even cooler.

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