The Dark Matter Time Projection Chamber (DMTPC) is a low pressure (75 Torr CF4) 10 liter detector capable of measuring the vector direction of nuclear recoils with the goal of directional dark matter detection. In this paper we present the first dark matter limit from DMTPC. In an analysis window of 80-200 keV recoil energy, based on a 35.7 g-day exposure, we set a 90% C.L. upper limit on the spin-dependent WIMP-proton cross section of 2.0 x 10^{-33} cm^{2} for 115 GeV/c^2 dark matter particle mass.