  We present the results of a new reverberation mapping campaign for the
broad-lined active galactic nucleus (AGN) in the edge-on spiral IC4329A.
Monitoring of the optical continuum with $V-$band photometry and broad
emission-line flux variability with moderate-resolution spectroscopy allowed
emission-line light curves to be measured for H$\beta$, H$\gamma$, and HeII
$\lambda 4686$. We find a time delay of $16.3^{+2.6}_{-2.3}$ days for H$\beta$,
a similar time delay of $16.0^{+4.8}_{-2.6}$ days for H$\gamma$, and an
unresolved time delay of $-0.6^{+3.9}_{-3.9}$ days for HeII. The time delay for
H$\beta$ is consistent with the predicted value from the relationship between
AGN luminosity and broad line region radius, after correction for the
$\sim2.4$mag of intrinsic extinction at 5100A. Combining the measured time
delay for H$\beta$ with the broad emission line width and an adopted value of
$\langle f \rangle = 4.8$, we find a central supermassive black hole mass of
$M_{\rm BH}=6.8^{+1.2}_{-1.1}\times10^7 M_{\rm \odot}$. Velocity-resolved time
delays were measured across the broad H$\beta$ emission-line profile and may be
consistent with an ''M''-like shape. Modeling of the full reverberation
response of H$\beta$ was able to provide only modest constraints on some
parameters, but does exhibit agreement with the black hole mass and average
time delay. The models also suggest that the AGN structure is misaligned by a
large amount from the edge-on galaxy disk. This is consistent with expectations
from the unified model of AGNs, in which broad emission lines are expected to
be visible only for AGNs that are viewed at relatively face-on inclinations.
