  We calculate the melting line of the pancake-vortex system in a layered
superconductor, interpolating between two-dimensional (2D) melting at high
fields and the zero-field limit of single-stack evaporation. Long-range
interactions between pancake vortices in different layers permit a mean-field
approach, the ``substrate model'', where each 2D crystal fluctuates in a
substrate potential due to the vortices in other layers. We find the thermal
stability limit of the 3D solid, and compare the free energy to a 2D liquid to
determine the first-order melting transition and its jump in entropy.
