  We report specific heat measurements of the organic superconductors
$\kappa$-(ET)$_2$Cu(NCS)$_2$ and $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br. When the
magnetic field is rotated in the highly conducting planes at low temperature
($T\simeq 0.4$ K), we observe clear oscillations of specific heat which have a
strong fourfold component. The observed strong field and temperature dependence
of this fourfold component identifies it as originating from nodes in the
superconducting energy gap which point along the in-plane crystal axes
($d_{xy}$ symmetry)
