The pure rotational spectrum of MgSH was observed for the first time, using millimeter-wave absorption spectroscopy in the 280-365 GHz region. This short-lived gas phase free radical was produced in a high-temperature cell by the reaction of Mg metal vapor with H2S in the presence of an electrical discharge. The spectrum was analyzed using an S-reduced asymmetric rotor Hamiltonian to obtain molecular parameters, including rotational, centrifugal distortion, and spin-rotation constants. The analysis of the spectrum indicated that MgSH is bent, in agreement with an ab initio calculation. The angle Mg-S-H angle obtained from the analysis was 87.5 +/- 6.7 degrees, as compared to a calculated ab initio value of 91.1 degrees.