  We present a new model of magnetic reconnection in the presence of
turbulence, applicable when the magnetic helicity is non-zero. The new model
differs from the Lazarian-Vishniac turbulent reconnection theory by emphasizing
the role of locally coherent magnetic structures, whose existence is shown to
be permitted by the properties of magnetic field line separation in turbulent
plasma. Local coherence allows storage of magnetic helicity inside the
reconnection layer and we argue that helicity conservation produces locally
coherent twisted flux ropes. We then introduce the "Alfv\'en horizon" to
explain why the global reconnection rate can be governed by locally coherent
magnetic field structure instead of by field line wandering, formally extending
to 3D the principle that reconnection can be made fast by fragmentation of the
global current layer. Coherence is shown to dominate over field line dispersion
if the anisotropy of the turbulence at the perpendicular scale matching the
thickness of a marginally stable current layer exceeds the aspect ratio of the
current layer. Finally, we conjecture that turbulence generated within the
reconnection layer may produce a balance of anisotropies that maintains the
system in the flux-rope mediated regime. The new model successfully accounts
for the major features of 3D numerical simulations of self-generated turbulent
reconnection, including reconnection rates of 0.01 in resistive MHD and 0.1
with collisionless physics.
