  We present H$\alpha$-derived star-formation rates (SFRs) for the galaxy
cluster CL J0023+0423B at $z = 0.845$. Our $3\sigma$ flux limits corresponds to
a star-formation rate of 0.24 \smy, and our minimum reliable H$\alpha$ + [N II]
equivalent width is $> 10$ \AA, demonstrating that near-infrared narrow-band
imaging can sample the star-forming galaxy population in distant clusters.
Comparison with spectroscopy shows that the number of false detections is low
($9 \pm 6$%) and that our H$\alpha$ equivalent widths are correlated with
spectroscopically determined [O II] equivalent widths. A magnitude-limited
spectroscopic survey conducted over the same area missed 70% of the
star-forming galaxies and 65% of the integrated star formation. Using Hubble
Space Telescope Wide Field Planetary Camera 2 Archive images, we fit Sersic
profiles to all galaxies with significant narrow-band equivalent widths and
find that equivalent width decreases as the steepness of galaxy profile
increases. We find no significant population of early type galaxies with
ongoing star formation. The integrated SFR per cluster mass of CL J0023+0423B
is a factor of ten higher than that of the three $z \sim 0.2$ clusters in the
literature with available H$\alpha$ observations. A larger sample of $z \sim
0.8$ clusters spanning a range of cluster masses is needed to determine whether
this variation is due to a difference in cluster mass or redshift.
