  We present spectroscopic observations from the Hubble Space Telescope that
reveal for the first time the presence of a broad pedestal of Balmer-line
emission in the LINER galaxy NGC 4203. The emission-line profile is suggestive
of a relativistic accretion disk, and is reminiscent of double-peaked transient
Balmer emission observed in a handful of other LINERs. The very broad line
emission thus constitutes clear qualitative evidence for a black hole, and
spatially resolved narrow-line emission in NGC 4203 can be used to constrain
its mass, with M_BH less than 6 x 10^6 solar masses at 99.7% confidence. This
value implies a ratio of black-hole mass to bulge mass of less than
approximately 7 x 10^-4 in NGC 4203, which is less by a factor of ~3 - 9 than
the mean ratio obtained for other galaxies. The availability of an independent
constraint on central black-hole mass makes NGC4203 an important testbed for
probing the physics of weak active galactic nuclei. Assuming M_BH near the
detection limit, the ratio of observed luminosity to the Eddington luminosity
is approximately 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 observed double-peaked line emission.
Follow-up observations will make it possible to improve the black-hole mass
estimate and study variability in the nuclear emission.
