The COMPASS Collaboration at CERN has measured diffractive dissociation of 190 GeV/c pions into the π(-)π(-)π(+) final state using a stationary hydrogen target. A partial-wave analysis (PWA) was performed in bins of 3π mass and four-momentum transfer using the isobar model and the so far largest PWA model consisting of 88 waves. A narrow peak is observed in the f0(980)π channel with spin, parity and C-parity quantum numbers J(PC)=1(++). We present a resonance-model study of a subset of the spin-density matrix selecting 3π states with J(PC)=2(++) and 4(++) decaying into ρ(770)π and with J(PC)=1(++) decaying into f0(980)π. We identify a new a1 meson with mass (1414(-13)(+15)) MeV/c2 and width (153(-23)(+8)) MeV/c2. Within the final states investigated in our analysis, we observe the new a1(1420) decaying only into f0(980)π, suggesting its exotic nature.