A nonlinear, stochastic MHD model is suggested as an explanation for magnetic reconnection in the nearly collisionless environment of space plasma. The magnetic field line stochasticity (diffusion) results from the existence of overlapping k⋅B0(x)=0 resonances and provides the anomalous resistivity driving the reconnection. The field lines diffuse in bundles which derive directly, via a nonlinear MHD instability, from the turbulent mixing of the large-scale fields. The model is a purely self-consistent MHD model in which the dynamical invariants of one fluid MHD are satisfied. No ad hoc or kinetic instability-driven anomalous resistivity is required. Anomalous dissipation and reconnection are generated by a coarse-graining of the stochastic fields. The model is an example of ''topological dissipation'' of magnetic fields (Parker, 1972). Reconnection rates at a fraction of the Alfv¿n speed are predicted, and are in accord with previous conjecture (Parker, 1973). ¿ American Geophysical Union 1992