We present spectroscopic observations from the Hubble Space Telescope that
reveal for the first time the presence of a broad pedestal of Balmer line e
mission in the LINER galaxy NGC 4203. The emission-line profile is suggesti
ve of a relativistic accretion disk and is reminiscent of double-peaked tra
nsient Balmer emission observed in a handful of other LINERs. The very broa
d line emission thus constitutes clear qualitative evidence for a black hol
e, and spatially resolved narrow-line emission in NGC 4203 can be used to c
onstrain its mass, M-BH less than or equal to 6 x 10(6) M-circle dot, at 99
.7% confidence. This value implies a ratio of black hole mass to bulge mass
of less than or similar to 7 x 10(-4) in NGC 4203, which is less by a fact
or of similar to 3-9 than the mean ratio obtained for other galaxies. The a
vailability of an independent constraint on central black hole mass makes N
GC 4203 an important testbed for probing the physics of weak active galacti
c nuclei. Assuming M-BH near the detection limit, the ratio of the observed
luminosity to the Eddington luminosity is similar to 10(-4). This value is
consistent with advection-dominated accretion and hence with scenarios in
which an ion torus irradiates an outer accretion disk that produces the obs
erved double-peaked line emission. Follow-up observations will make it poss
ible to improve the black hole mass estimate and study variability in the n
uclear emission.