The Seyfert 1 galaxy Zw 229-015 is among the brightest active galaxies being monitored by the Kepler mission. In order to determine the black hole mass in Zw 229-015 from Hβ reverberation mapping, we have carried out nightly observations with the Kast Spectrograph at the Lick 3 m telescope during the dark runs from 2010 June through December, obtaining 54 spectroscopic observations in total. We have also obtained nightly V-band imaging with the Katzman Automatic Imaging Telescope at Lick Observatory and with the 0.9 m telescope at the Brigham Young University West Mountain Observatory over the same period. We detect strong variability in the source, which exhibited more than a factor of two change in broad Hβ flux. From cross-correlation measurements, we find that the Hβ light curve has a rest-frame lag of 3.86+0.69-0.90 days with respect to the V-band continuum variations. We also measure reverberation lags for Hα and Hγ and find an upper limit to the Hδ lag. Combining the Hβ lag measurement with a broad Hβ width of σline = 1590 ± 47 km s-1 measured from the rms variability spectrum, we obtain a virial estimate of M BH = 1.00+0.19-0.24 × 107 M⊙ for the black hole in Zw 229-015. As a Kepler target, Zw 229-015 will eventually have one of the highest-quality optical light curves ever measured for any active galaxy, and the black hole mass determined from reverberation mapping will serve as a benchmark for testing relationships between black hole mass and continuum variability characteristics in active galactic nuclei. © 2011. The American Astronomical Society. All rights reserved.