We present 3D-HST, a near-infrared spectroscopic Treasury program with the Hubble Space Telescope for studying the physical processes that shape galaxies in the distant universe. 3D-HST provides rest-frame optical spectra for a sample of ∼7000 galaxies at 1 < z < 3.5, the epoch when 60% of all star formation took place, the number density of quasars peaked, the first galaxies stopped forming stars, and the structural regularity that we see in galaxies today must have emerged. 3D-HST will cover three quarters (625arcmin 2) of the CANDELS Treasury survey area with two orbits of primary WFC3/G141 grism coverage and two to four orbits with the ACS/G800L grism in parallel. In the IR, these exposure times yield a continuum signal-to-noise ratio of 5per resolution element at H 140 ∼ 23.1 and a 5σ emission-line sensitivity of ∼5 × 10 -17 erg s -1 cm -2 for typical objects, improving by a factor of ∼2 for compact sources in images with low sky background levels. The WFC3/G141 spectra provide continuous wavelength coverage from 1.1 to 1.6 μm at a spatial resolution of ∼0″.13, which, combined with their depth, makes them a unique resource for studying galaxy evolution. We present an overview of the preliminary reduction and analysis of the grism observations, including emission-line and redshift measurements from combined fits to the extracted grism spectra and photometry from ancillary multi-wavelength catalogs. The present analysis yields redshift estimates with a precision of σ(z) = 0.0034(1 + z), or σ(v) 1000kms -1. We illustrate how the generalized nature of the survey yields near-infrared spectra of remarkable quality for many different types of objects, including a quasar at z = 4.7, quiescent galaxies at z ∼ 2, and the most distant T-type brown dwarf star known. The combination of the CANDELS and 3D-HST surveys will provide the definitive imaging and spectroscopic data set for studies of the 1 < z < 3.5 universe until the launch of the James Webb Space Telescope.