The "island of inversion" nucleus 32 Mg has been studied by a (t, p) two neutron transfer reaction in inverse kinematics at REX-ISOLDE. The shape coexistent excited 0+ state in 32 Mg has been identified by the characteristic angular distribution of the protons of the Δ L=0 transfer. The excitation energy of 1058 keV is much lower than predicted by any theoretical model. The low γ-ray intensity observed for the decay of this 0+ state indicates a lifetime of more than 10 ns. Deduced spectroscopic amplitudes are compared with occupation numbers from shell-model calculations.