The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the π- π- π+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420,000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV2/c2. The well-known resonances a1(1260), a2(1320), and π2(1670) are clearly observed. In addition, the data show a significant natural-parity exchange production of a resonance with spin-exotic quantum numbers J(PC)=1-+ at 1.66 GeV/c2 decaying to ρπ. The resonant nature of this wave is evident from the mass-dependent phase differences to the J(PC)=2-+ and 1++ waves. From a mass-dependent fit a resonance mass of (1660±10(-64)(+0)) MeV/c2 and a width of (269±21(-64)(+42)) MeV/c2 are deduced, with an intensity of (1.7±0.2)% of the total intensity.