This paper describes the methods and goals of the spectroscopy programme of COMPASS using hadron beams, and reports on first results from a short pilot run using a 190 GeV/c pion beam, carried out in 2004. A partial wave analysis of the reaction π-N → π-π-π+ N' shows significant production of a state with spin-exotic quantum numbers JPC = 1-+ at 1.6 GeV/c2.