  Markarian 421 (Mrk 421) was the first blazar detected at gamma-ray energies
above 300 GeV, and it remains one of only twelve TeV blazars detected to date.
TeV gamma-ray measurements of its flaring activity and spectral variability
have placed constraints on models of the high-energy emission from blazars.
However, observations between 50 and 300 GeV are rare, and the high-energy peak
of the spectral energy distribution (SED), predicted to be in this range, has
never been directly detected. We present a detection of Mrk 421 above 100 GeV
as made by the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE)
during a multiwavelength campaign in early 2004. STACEE is a ground-based
atmospheric Cherenkov telescope using the wavefront sampling technique to
detect gamma rays at lower energies than achieved by most imaging Cherenkov
telescopes. We also outline a method for reconstructing gamma-ray energies
using a solar heliostat telescope. This technique was applied to the 2004 data,
and we present the differential energy spectrum of Mrk 421 above 130 GeV.
Assuming a differential photon flux dN/dE proportional to E^-a, we measure a
spectral index a = 2.1 +/- 0.2 (statistical) +0.2/-0.1 (systematic). Finally,
we discuss the STACEE spectrum in the context of the multiwavelength results
from the same epoch.
