Continuous 3d Freezing Transition in Layered Superconductors

We use Ginzburg-Landau theory to study the $H_{c2}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3d freezing transition to a triangular vortex super-solid in the three-dimensional XY universality class. If screening effects are neglected, off--diagonal--long--range--order survives only for $d>d_{lc}=5/2$. The partial breaking of the lowest Landau level degeneracy induced by layering leads to a {\sl local} selection of a triangular lattice structure, in contrast to the {\sl global} free energy minimization in, e.g. Abrikosov's calculation. Our results are relevant to artificially layered superconductors and to strongly anisotropic high T$_c$ materials.