We present the first results from the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) Grism Parallel Survey, a large program obtaining deep, slitless ACS grism spectroscopy of high-latitude HST parallel fields. We report on 11 high Galactic latitude fields here, each with grism integration times of more than 12 ks. We identify 601 compact emission-line galaxies at z ≤ 1.6, reaching emission lines to a flux limit of 5 × 10^-18 ergs cm^-2 s^-1 (3 σ). We determine redshifts by cross-correlation of the target spectra with template spectra, followed by visual inspection. We measure star formation rates from the observed [O II] λ3727, [O III] λ5007, and Hα line fluxes. Follow-up observations with the Keck telescope of one of the survey fields confirms our classification and redshifts with σ(z) 0.02. This is one of the deepest emission-line surveys to date, covering a total area of 121 arcmin². The rough estimate of the comoving number density of emission-line galaxies in our survey at 0.3 < z < 1.3 is ~4.5 × 10^-3 h Mpc^-3. We reach deeper into the emission-line luminosity function than either the STIS or NICMOS grism parallel surveys, finding an apparent space density of emission-line galaxies several times higher than those surveys. Because of the ACS high spatial resolution, our survey is very sensitive to faint, compact galaxies with strong emission lines and weak continua. The ACS grism survey provides the comoving star formation density at z ≤ 1.6 at a high level of completeness.