  We present high angular resolution (0.3" or 37 pc) Atacama Large
Millimeter/sub-millimeter Array (ALMA) observations of the CO(2-1) line
emission from a central disc in the early-type galaxy NGC 524. This disc is
shown to be dynamically relaxed, exhibiting ordered rotation about a compact
1.3mm continuum source, which we identify as emission from an active
supermassive black hole (SMBH). There is a hole at the centre of the disc
slightly larger than the SMBH sphere of influence. An azimuthal distortion of
the observed velocity field is found to be due to either a position angle warp
or radial gas flow over the inner 2.5". By forward-modelling the observations,
we obtain an estimate of the SMBH mass of
$4.0^{+3.5}_{-2.0}\times10^8\,\mathrm{M_\odot}$, where the uncertainties are at
the $3\sigma$ level. The uncertainties are dominated by the poorly constrained
inclination and the stellar mass-to-light ratio of this galaxy, and our
measurement is consistent with the established correlation between SMBH mass
and stellar velocity dispersion. Our result is roughly half that of the
previous stellar dynamical measurement, but is consistent within the
uncertainties of both. We also present and apply a new tool for modelling
complex molecular gas distributions.
