A new hybrid classical/quantum method is proposed and applied to investigate the vibrational predissociation (VP) dynamics of the He2Cl2 complex. The full dimensionality of the system (assuming zero total angular momentum) is included in the method. The VP process of He2Cl2 is dominated by a sequential mechanism of dissociation of the two van der Waals bonds. The hybrid approach describes the first weak bond fragmentation classically, and the second one quantum mechanically. The rotational distribution of the Cl-2 fragment is calculated both with the hybrid method and with a fully classical trajectory simulation, and compared with the experimental distribution. The hybrid distribution is found to agree very well with the experimental one, and to involve a substantial improvement with respect to the classical result.