  We present magnetic-torque experiments on the organic superconductor
k-(BEDT-TTF)2Cu(NCS)2 for magnetic fields applied parallel to the 2D
superconducting layers. The experiments show a crossover from a second-order to
a first-order transition when the upper critical field reaches 21 T. Beyond
this field, which we interpret as the Pauli limit for superconductivity, the
upper critical field line shows a pro-nounced upturn and a phase transition
line separates the superconducting state into a low- and a high-field phase. We
interpret the data in the framework of a Fulde-Ferrell-Larkin-Ovchinnikov
state.
