  As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM)
project we present an estimate of the mass of the supermassive black hole
(SMBH) in the nearby fast-rotating early-type galaxy NGC4429, that is barred
and has a boxy/peanut-shaped bulge. This estimate is based on Atacama Large
Millimeter/submillimeter Array (ALMA) cycle-2 observations of the 12CO(3-2)
emission line with a linear resolution of ~13 pc (0"18x0"14). NGC4429 has a
relaxed, flocculent nuclear disc of molecular gas that is truncated at small
radii, likely due to the combined effects of gas stability and tidal shear. The
warm/dense 12CO(3-2) emitting gas is confined to the inner parts of this disc,
likely again because the gas becomes more stable at larger radii, preventing
star formation. The gas disc has a low velocity dispersion of
2.2$^{+0.68}_{-0.65}$ km/s. Despite the inner truncation of the gas disc, we
are able to model the kinematics of the gas and estimate a mass of
(1.5$\pm0.1^{+0.15}_{-0.35}$)$\times$10$^8$ Msun for the SMBH in NGC4429 (where
the quoted uncertainties reflect the random and systematic uncertainties,
respectively), consistent with a previous upper limit set using ionised gas
kinematics. We confirm that the V-band mass-to-light ratio changes by ~30%
within the inner 400 pc of NGC4429, as suggested by other authors. This SMBH
mass measurement based on molecular gas kinematics, the sixth presented in the
literature, once again demonstrates the power of ALMA to constrain SMBH masses.
