  We present a sample of 1165 extreme emission-line galaxies (EELGs) at 4<z<9
selected using James Webb Space Telescope (JWST) NIRCam photometry in the
Cosmic Evolution Early Release Science (CEERS) program. We use a simple method
to photometrically identify EELGs with Hb + [OIII] (combined) or Ha emission of
observed-frame equivalent width EW >5000 AA. JWST/NIRSpec spectroscopic
observations of a subset (34) of the photometrically selected EELGs validate
our selection method: all spectroscopically observed EELGs confirm our
photometric identification of extreme emission, including some cases where the
SED-derived photometric redshifts are incorrect. We find that the medium-band
F410M filter in CEERS is particularly efficient at identifying EELGs, both in
terms of including emission lines in the filter and in correctly identifying
the continuum between Hb + [OIII] and Ha in the neighboring broad-band filters.
We present examples of EELGs that could be incorrectly classified at ultra-high
redshift (z>12) as a result of extreme Hb + [OIII] emission blended across the
reddest photometric filters. We compare the EELGs to the broader (sub-extreme)
galaxy population in the same redshift range and find that they are consistent
with being the bluer, high equivalent width tail of a broader population of
emission-line galaxies. The highest-EW EELGs tend to have more compact
emission-line sizes than continuum sizes, suggesting that active galactic
nuclei are responsible for at least some of the most extreme EELGs.
Photometrically inferred emission-line ratios are consistent with ISM
conditions with high ionization and moderately low metallicity, consistent with
previous spectroscopic studies.
