We present optical observations of the low-luminosity Seyfert 1 nucleus of NGC 4395, as part of a multiwavelength reverberation-mapping program. Observations were carried out over two nights in 2004 April at Lick, Wise, and Kitt Peak Observatories. We obtained V-band and B-band photometry, and spectra over the range 3500-6800 Angstroms. Simultaneous Hubble Space Telescope UV and Chandra X-ray observations are presented in companion papers. Even though NGC 4395 was in an extremely low state of activity, we detect significant continuum variability of 2-10%, increasing toward shorter wavelengths. The continuum light curves, both spectroscopic and photometric, are qualitatively similar to the simultaneous UV and X-ray light curves. Inter-band cross-correlations suggest that the optical continuum emission lags behind the UV continuum emission by 24 +7/-9 min, and that the optical continuum emission lags behind the X-ray continuum emission by 44 +/- 13 min, consistent with a reprocessing model for active galactic nucleus emission. There are also hints of Balmer emission lines lagging behind the optical continuum by an amount slightly larger than the emission-line lag detected in the UV. These results are all similar to those of other Seyfert 1 nuclei. The emission-line lag yields a mass measurement of the central black hole, which although not very significant, is consistent with the value derived from the simultaneous UV data.