  Single crystals of the layered organic type II superconductor,
$\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, have been studied in magnetic fields of
up to 33 T and at temperatures between 0.5 K and 11 K using a compact
differential susceptometer. When the magnetic field lies precisely in the
quasi-two-dimensional planes of the material, there is strong evidence for a
phase transition from the superconducting mixed state into a
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, manisfested as a change in the
rigidity of the vortex system. The behaviour of the transition as a function of
temperature is in good agreement with theoretical predictions.
