  We present a high precision H-band emission spectrum of the transiting brown
dwarf KELT-1b, which we spectrophotometrically observed during a single
secondary eclipse using the LUCI1 multi-object spectrograph on the Large
Binocular Telescope. Using a Gaussian-process regression model, we are able to
clearly measure the broadband eclipse depth as Delta-H=1418+/-94ppm. We are
also able to spectrally-resolve the H-band into five separate wavechannels and
measure the eclipse spectrum of KELT-1b at R~50 with an average precision of
+/-135ppm. We find that the day side has an average brightness temperature of
3250+/-50K, with significant variation as a function of wavelength. Based on
our observations, and previous measurements of KELT-1b's eclipse at other
wavelengths, we find that KELT-1b's day side appears identical to an isolated
3200K brown dwarf, and our modeling of the atmospheric emission shows a
monotonically decreasing temperature-pressure profile. This is in contrast to
hot Jupiters with similar day side brightness temperatures near 3000K, all of
which appear to be either isothermal or posses a stratospheric temperature
inversion. We hypothesize that the lack of an inversion in KELT-1b is due to
its high surface gravity, which we argue could be caused by the increased
efficiency of cold-trap processes within its atmosphere.
