  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 $z\sim3.5$. We identify 60 galaxies that
comprise a composite SED with [OIII]+H$\beta$ rest-frame equivalent width of
$803\pm228$\AA\ and another 218 galaxies in a composite SED with equivalent
width of $230\pm90$\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.
