We present a catalog of 208 0.3 z <2.1 emission-line galaxies (ELGs) selected from 1D slitless spectroscopy obtained using Hubble's WFC3 G102 grism, as part of the Faint Infrared Grism Survey. We identify ELG candidates by searching for significant peaks in all continuum-subtracted G102 spectra and, where possible, confirm candidates by identifying consistent emission lines in other available spectra or with published spectroscopic redshifts. We provide derived emission-line fluxes and errors, redshifts, and equivalent widths for H alpha lambda 6563, [O iii] lambda lambda 4959, 5007, and [O ii] lambda 3727 emission lines, for ELGs down to AB(F105W) >28 and >10(-17) erg cm(-2) s(-1) line flux. We use the resulting line catalog to investigate a possible relationship between line emission and a galaxy's environment. We use seventh-nearest-neighbor distances to investigate the typical surroundings of ELGs compared to non-ELGs, and we find that [O iii] emitters are preferentially found at intermediate galaxy densities near galaxy groups. We characterize these ELGs in terms of the galaxy specific star formation rate (SFR) versus stellar mass and find no significant influence of environment on that relation. We calculate SFRs and find no dependence of SFR on local galaxy surface density for 0.3 z alpha emitters and for 0.8 z iii] emitters. We find similar rates of close-pair interaction between ELGs and non-ELGs. For galaxy surface densities sigma