Antiproton-proton annihilation at rest into π+ π- π0 has been studied by stopping antiprotons from LEAR in a H2 gas target at normal temperature and pressure. The reaction is observed in coincidence with L X-rays which are emitted in the cascade of {Mathematical expression} atoms. The X-rays populate one of the angular momentum L=1 states of a {Mathematical expression} atom which then annihilates. A spinparity analysis of the π+ π- π0 Dalitz plot gives contributions from the three P states from which annihilation into three pions is allowed. The most striking features of the Dalitz plot are production of charged and neutral ρ{variant}(770) and of f2(1270) mesons. Production of ρ{variant}(770) mesons proceeds via the isoscalar part of the1P1 state and the isovector part of the3P1 state. f2(1270) mesons are produced abundantly from P states while their production from S states is very weak. The π+ π- invariant mass spectrum shows a third strong peak at a mass of 1565±20 MeV/c2 and a width of 170±40 MeV/c2, which we call AX(1565). No reasonable description of the Dalitz plot is obtained without introducing the AX(1565) as a new isoscalar particle. A phase shift analysis shows a phase movement which is fully compatible with a resonance with JPC=2++. The most likely interpretation of the new resonance is a multiquark {Mathematical expression} state. © 1990 Springer-Verlag.