We have performed detailed studies of the angle- and temperature-dependent resistive upper critical fields in the layered organic superconductor κ-(BEDT-TTF)2Cu(NCS)2. With the magnetic field lying in the conducting planes, our measurements show an upper critical field which comfortably exceeds the Pauli-paramagnetic limit in this material. We find no azimuthal angle dependence of the critical field, in spite of recent evidence that this material has gap nodes characteristic of d-wave superconductivity. We propose that the large critical fields may be due to a Fulde-Ferrell-Larkin-Ovchinnikov state which can exist in exactly in-plane fields because of the nature of the Fermi surface of κ-(BEDT-TTF)2Cu(NCS)2. © 1999 IOP Publishing Ltd.