We present recent optical spectroscopy of the nucleus of the spiral galaxy M81 obtained with the post-COSTAR Faint Object Spectrograph (FOS) aboard Hubble Space Telescope (HST). The spectra reveal a new double-peaked broad component in the profiles of H alpha and H beta, the FWZI of which are approximate to 14 000 and 11 000 km s(-1), respectively. Such double-peaked broad emission lines are known to exist in some active galactic nuclei (AGNs) classified as broad-line radio galaxies or radio-loud quasars, but M81 is only the second AGN with low radio power and in a spiral host galaxy known to exhibit such lines. This detection in M81 strongly supports the trend for such double-peaked broad lines to be found preferentially in galactic nuclei with LINER-like narrow emission-line spectra. We emphasize that all AGNs known to exhibit broad, double-peaked line profiles also show clear evidence for jets, even though these jets may not be luminous radio emitters. In M81, the red peak of the double-peaked profile is stronger than the blue peak, while the blue wing extends further from systemic velocity than does the red wing. These properties are contrary to the prediction of a model in which the line originates in a circular, relativistic accretion disk. Either the disk is elliptical or the double-peaked line originates in a bipolar outflow (e.g., jets). Continued spectroscopic monitoring of the broad H alpha profile in M81 is needed to constrain such models. (C) 1996 American Astronomical Society.