  We have obtained spectra of three QSO/AGNs with the GHRS aboard the Hubble
Space Telescope to search for absorption from low column density gas in the
halo of the dwarf spheroidal (dSph) galaxy Leo I. The probe sightlines pass
2.1, 3.7, and 8.1 kpc from the center of the galaxy, but no CIV, SiII, or SiIV
absorption is found at the velocity of Leo I. The absence of low ionization
species suggests that the column density of neutral hydrogen which exists
within 2-4 kpc of the galaxy is N(HI) < 10^{17} cm^{-2}; assuming that the high
ionization lines of SiIV and CIV dominate the ionization fraction of silicon
and carbon, the limit to the total hydrogen column is N(H) < 10^{18} cm^{-2}.
Our results demonstrate that there are no dense flows of gas in or out of Leo
I, and that there is no evidence for tidally disrupted gas which might have
accompanied the galaxy's formation or evolution. However, our detection limits
are insufficient to rule out the existence of a sphere or shell of ionized gas
around the dSph, with a mass up to that constituting the entire galaxy. Our
models show that dSph galaxies similar to Leo I are not massive enough to have
halos which can contribute significantly to the metal line absorption
cross-section of QSO absorbers seen at high redshift.
