A reverberation-mapping program on NGC 4395, the least luminous known Seyfert 1 galaxy, undertaken with the Space Telescope Imaging Spectrograph on the Hubble Space Telescope yields a measurement of the mass of the central black hole M_BH_=(3.6+/-1.1)x10^5^M_{sun}_. The observations consist of two visits of five orbits each, in 2004 April and July. During each of these visits, the UV continuum varied by at least 10% (rms), and only C IV {lambda}1549 showed corresponding variations large enough to reliably determine the emission-line lag, which was measured to be of order 1-hr for both visits.