In this paper we present the MOSFIRE Deep Evolution Field (MOSDEF) survey. The MOSDEF survey aims to obtain moderate-resolution (R = 3000-3650) rest-frame optical spectra (∼3700-7000 ) for ∼1500 galaxies at in three well-studied CANDELS fields: AEGIS, COSMOS, and GOODS-N. Targets are selected in three redshift intervals:, down to fixed (F160W) magnitudes of 24.0, 24.5, and 25.0, respectively, using the photometric and spectroscopic catalogs from the 3D-HST survey. We target both strong nebular emission lines (e.g., [O ii], Hβ, [O iii], H, [N ii], and [S ii]) and stellar continuum and absorption features (e.g., Balmer lines, Ca-ii H and K, Mgb, 4000 break). Here we present an overview of our survey, the observational strategy, the data reduction and analysis, and the sample characteristics based on spectra obtained during the first 24 nights. To date, we have completed 21 masks, obtaining spectra for 591 galaxies. For ∼80% of the targets we derive a robust redshift from either emission or absorption lines. In addition, we confirm 55 additional galaxies, which were serendipitously detected. The MOSDEF galaxy sample includes unobscured star-forming, dusty star-forming, and quiescent galaxies and spans a wide range in stellar mass () and star formation rate. The spectroscopically confirmed sample is roughly representative of an H-band limited galaxy sample at these redshifts. With its large sample size, broad diversity in galaxy properties, and wealth of available ancillary data, MOSDEF will transform our understanding of the stellar, gaseous, metal, dust, and black hole content of galaxies during the time when the universe was most active.