Atmospheric studies of spectroscopically accessible terrestrial exoplanets lay the groundwork for comparative planetology between these worlds and the solar system terrestrial planets. LHS3844b is a highly irradiated terrestrial exoplanet (R=1.303{+/-}0.022R{Earth}) orbiting a mid-M dwarf 15parsecs away. Work based on near-infrared Spitzer phase curves ruled out atmospheres with surface pressures >~10bars on this planet. We present 13 transit observations of LHS3844b taken with the Magellan Clay telescope and the LDSS3C multi-object spectrograph covering 620-1020nm. We analyze each of the 13 data sets individually using a Gaussian process regression, and present both white and spectroscopic light curves. In the combined white light curve we achieve an rms precision of 65ppm when binning to 10minutes. The mean white light-curve value of (Rp/Rs)^2^ is 0.4170{+/-}0.0046%. To construct the transmission spectrum, we split the white light curves into 20 spectrophotometric bands, each spanning 20nm, and compute the mean values of (Rp/Rs)^2^ in each band. We compare the transmission spectrum to two sets of atmospheric models. We disfavor a clear, solar composition atmosphere ({mu}=2.34) with surface pressures >~0.1bar to 5.2{sigma} confidence. We disfavor a clear, H2O steam atmosphere ({mu}=18) with surface pressures >~0.1bar to low confidence (2.9{sigma}). Our observed transmission spectrum favors a flat line. For solar composition atmospheres with surface pressures >~1bar we rule out clouds with cloud-top pressures of 0.1bar (5.3{sigma}), but we cannot address high-altitude clouds at lower pressures. Our results add further evidence that LHS3844b is devoid of an atmosphere.