We report the discovery of an extremely broad H alpha emission line in the
LINER nucleus of NGC 4579. From ground-based observations, the galaxy was p
reviously known to contain a type 1 nucleus with a broad H alpha line of FW
HM approximate to 2300 km s(-1) and FWZI approximate to 5000 km s(-1). New
spectra obtained with the Hubble Space Telescope (HST) and a 0.2" wide slit
reveal an H alpha component with an FWZI of similar to 18,000 km s(-1). Th
e line is not obviously double peaked, but it does possess "shoulders" on t
he red and blue sides which resemble the profiles seen in double-peaked emi
tters such as NGC 4203 and NGC 4450. This similarity suggests that the very
broad H alpha profile in NGC 4579 may represent emission from an accretion
disk. Three such objects have been found recently in two HST programs whic
h have targeted a total of 30 galaxies, demonstrating that double-peaked or
extremely broad-line emission in LINERs must be much more common than woul
d be inferred from ground-based surveys. The ratio of the narrow [S II] lam
bda lambda 6716, 6731 lines shows a pronounced gradient indicating a steep
rise in density toward the nucleus. The direct detection of a density gradi
ent within the inner arcsecond of the narrow-line region confirms expectati
ons from previous observations of line width-critical density correlations
in several LINERs.