 Møller was twice a Nordic Champion, winning at Copenhagen 1899 (2nd Nord-ch) and at Gothenburg 1901 (3rd Nord-ch).At the beginning of his career, he tied for 4-5th at Copenhagen 1895 (Andreas Rosendahl won), took 2nd, behind Sven Otto Svensson, at Stockholm 1897 (1st Nordic-ch), and took 4th at Copenhagen 1907 (6th Nord-ch, Paul Leonhardt won).In 1920, he tied for 13-14th in Gothenburg (Richard Réti won).