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 \pm 94 ppm . We are also able to spectrally-resolve the H -band into five separate wavechannels and measure the eclipse spectrum of KELT-1b at R \approx 50 with an average precision of \pm 135 ppm . We find that the day side has an average brightness temperature of 3250 \pm 50 K , 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 3200 K 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 3000 K , 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 .