  We present a nearly perfect Pauli-limited critical field phase diagram for
the anisotropic organic superconductor \$\alpha$-(ET)$_2$NH$_4$(SCN)$_4$ when
the applied magnetic field is oriented parallel to the conducting layers. The
critical fields (${H_{c_2}$) were found by use of penetration depth
measurements. Because ${H_{c_2}$ is Pauli-limited, the size of the
superconducting energy gap can be calculated. The role of spin-orbit scattering
and many-body effects play a role in explaining our measurements.
