Using deep multi-wavelength photometry of galaxies from ZFOURGE, we group galaxies at $2.5<z<4.0$ by the shape of their spectral energy distributions (SEDs). We identify a population of galaxies with excess emission in the $K_s$-band, which corresponds to [OIII]+H$beta$ emission at $2.95<z<3.65$. This population includes 78% of the bluest galaxies with UV slopes steeper than $beta = -2$. We de-redshift and scale this photometry to build two composite SEDs, enabling us to measure equivalent widths of these Extreme [OIII]+H$beta$ Emission Line Galaxies (EELGs) at $zsim3.5$. We identify 60 galaxies that comprise a composite SED with [OIII]+H$beta$ rest-frame equivalent width of $803pm228$AA and another 218 galaxies in a composite SED with equivalent width of $230pm90$AA. These EELGs are analogous to the `green peas found in the SDSS, and are thought to be undergoing their first burst of star formation due to their blue colors ($beta < -1.6$), young ages ($log(rm{age}/yr)sim7.2$), and low dust attenuation values. Their strong nebular emission lines and compact sizes (typically $sim1.4$ kpc) are consistent with the properties of the star-forming galaxies possibly responsible for reionizing the universe at $z>6$. Many of the EELGs also exhibit Lyman-$alpha$ emission. Additionally, we find that many of these sources are clustered in an overdensity in the Chandra Deep Field South, with five spectroscopically confirmed members at $z=3.474 pm 0.004$. The spatial distribution and photometric redshifts of the ZFOURGE population further confirm the overdensity highlighted by the EELGs.
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