David Kilgour is quite simply one of the best purveyors of tuneful guitar pop to record since the advent of punk. His first band, the Clean, kick-started New Zealand’s underground music scene in 1981 when its first single, “Tally Ho!,” recorded at a cost of $50, topped that country’s charts for weeks without any radio play. Kilgour defined the band’s sound with three attributes: his singing, which effortlessly ranges from insouciant ennui to aching melancholy; his guitar playing, which encompasses a giddy rhythmic attack, brisk acoustic strumming, and explosive solo excursions that betray influences as diverse as Gram Parsons, Jimi Hendrix, the Velvet Underground, and the Beach Boys; and most of all his gift for writing simple, elegant, indelible melodies. The Clean broke up for the first time in 1982 (like a high school graduating class, they indulge in occasional brief reunions), and Kilgour’s subsequent bands (the Great Unwashed, Stephen, Pop Art Toasters) have mined one aspect or another of his first band’s territory with uniformly excellent results. Kilgour’s first solo album, 1992’s Here Come the Cars (Flying Nun), introduced a newfound warmth and gentle spaciousness to his repertoire. He’s touring in support of his second album, Sugar Mouth, which should be released in the U.S. this winter, and this show is his Chicago debut. Number One Cup and Eggs open. Sunday, 9 PM, Lounge Ax, 2438 N. Lincoln; 525-6620.