  Ultrasound velocity measurements of the unconventional superconductor
CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an
unusual structural transformation of the flux line lattice (FLL) in the
vicinity of the upper critical field. The transition field coincides with that
at which heat capacity measurements reveal a second order phase transition. The
lowering of the sound velocity at the transition is consistent with the
collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL
pinning. These results provide a strong evidence that the high field state is
the Fulde-Ferrel-Larkin-Ovchinikov phase, in which the order parameter is
spatially modulated and has planar nodes aligned perpendicular to the vortices.
