Fognini, who last week led Italy to a first-round Davis Cup victory over Argentina, posted a 6-4, 3-6, 6-2 triumph over Chardy on the red clay at Vina del Mar.
His next opponent will be third-seeded Nicolas Almagro of Spain, who had little trouble getting past Japanese qualifier Taro Daniel 6-2, 7-5.
He goes on to play Argentina's Leonardo Mayer, who advanced with a 3-6, 7-5, 6-3 decision over Daniel Gimeno-Traver of Spain.
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