We present deep images of the redshift z \ 0.41 galaxy cluster Abell 851 (Cl 0939]4713) including a narrow bandwidth image of the redshifted [O II] jj3726, 3729 line emission. The [O II] doublet is the most accessible tracer of star formation out to redshifts near unity, and we use it to identify candidates for star-forming galaxies. The galaxies selected lie within a projected clustercentric distance of 2 Mpc and have line-of-sight velocities with respect to the cluster in the range of^1460 km s~1. The sample is complete to magnitude for galaxies with emission-line equivalent widths greater than m 5129 (AB) \ 24.0 about 11 in the observed frame. The sample is contaminated by foreground galaxies with a steep 4000 A break across the Ðlters and possibly Lya emitters at z \ 3.31, but such galaxies can be identiÐed using A color, brightness, and equivalent-width criteria. Excluding the likely interlopers, the number density of star-forming galaxies near Cl 0939]4713 is still at least 3È4 times higher than that of a similar column through the Ðeld at z \ 0.4. Galaxies in the cluster sample have lower [O II] equivalent widths than similarly selected Ðeld galaxies at z D 0.4, however, and we suggest that while the density of galaxies is higher in the cluster the star formation activity in individual galaxies is suppressed relative to their counterparts in the Ðeld. The relatively small enhancement in the surface density of the [O II]-selected population toward the cluster core leads us to believe the [O II]-selected galaxies reside in the outer regions of the cluster. We identify a population of starburst galaxies among the [O II] emitters based on their blue g[i color. The majority of the [O II]-selected galaxies appear to be related to the normal spiral galaxy population, but the bursting population is dominated by intrinsically faint galaxies of below average size. We suggest that this population is composed primarily of dwarf galaxies and discuss their relation to the dwarf galaxies in present-day clusters.