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It is shown that in extremely anisotropic layered superconductors theinteraction of vortex lines with a parallel planar surface, which for straightlines along the c-axis decreases exponentially over the in-plane penetrationdepth $\lambda$, becomes a long-range dipole--dipole attraction when the vortexline is distorted randomly. This novel long-range fluctuation-inducedattraction enhances the thermal fluctuations down to depths much larger than$\lambda$ and may lead to flux creep towards the surface.Comment: 12 pages, RevTeX, a figure is attached as a postscript file, the  paper is accepted for publication in Physical Review Letter

Long-Range Fluctuation-Induced Attraction of Vortices to the Surface in Layered Superconductors