The multiplexing capability of slitless spectroscopy is a powerful asset in creating large spectroscopic data sets, but issues such as spectral confusion make the interpretation of the data challenging. Here we present a new method to search for emission lines in the slitless spectroscopic data from the 3D-HST survey utilizing the Wide-Field Camera 3 on board the Hubble Space Telescope. Using a novel statistical technique, we can detect compact (extended) emission lines at 90% completeness down to fluxes of 1.5(3.0)x10^-17^erg/s/cm^2^, close to the noise level of the grism exposures, for objects detected in the deep ancillary photometric data. Unlike previous methods, the Bayesian nature allows for probabilistic line identifications, namely redshift estimates, based on secondary emission line detections and/or photometric redshift priors. As a first application, we measure the comoving number density of Extreme Emission Line Galaxies (restframe [OIII]{lambda}5007 equivalent widths in excess of 500{AA}). We find that these galaxies are nearly 10x more common above z~1.5 than at z<~0.5. With upcoming large grism surveys such as Euclid and WFIRST, as well as grisms featured prominently on the NIRISS and NIRCam instruments on the James Webb Space Telescope, methods like the one presented here will be crucial for constructing emission line redshift catalogs in an automated and well-understood manner.