  The gas metallicity of galaxies is often estimated using strong emission
lines such as the optical lines of [OIII] and [OII]. The most common measure is
"R23", defined as ([OII]$\lambda$$\lambda$3726, 3729 +
[OIII]$\lambda$$\lambda$4959,5007)/H$\beta$. Most calibrations for these
strong-line metallicity indicators are for continuum selected galaxies. We
report a new empirical calibration of R23 for extreme emission-line galaxies
using a large sample of about 800 star-forming green pea galaxies with reliable
T$_e$-based gas-phase metallicity measurements. This sample is assembled from
Sloan Digital Sky Survey (SDSS) Data Release 13 with the equivalent width of
the line [OIII]$\lambda$5007 $>$ 300 \AA\ or the equivalent width of the line
H$\beta$ $>$ 100 \AA\ in the redshift range 0.011 $<$ z $<$ 0.411. For galaxies
with strong emission lines and large ionization parameter (which manifests as
log [OIII]$\lambda$$\lambda$4959,5007/[OII]$\lambda$$\lambda$3726,3729 $\geq$
0.6), R23 monotonically increases with log(O/H) and the double-value degeneracy
is broken. Our calibration provides metallicity estimates that are accurate to
within $\sim$ 0.14 dex in this regime. Many previous R23 calibrations are found
to have bias and large scatter for extreme emission-line galaxies. We give
formulae and plots to directly convert R23 and
[OIII]$\lambda$$\lambda$4959,5007/[OII]$\lambda$$\lambda$3726,3729 to log(O/H).
Since green peas are best nearby analogs of high-redshift Lyman-$\alpha$
emitting galaxies, the new calibration offers a good way to estimate the
metallicities of both extreme emission-line galaxies and high-redshift
Lyman-$\alpha$ emitting galaxies. We also report on 15 galaxies with
metallicities less than 1/12 solar, with the lowest metallicities being
12+log(O/H) = 7.25 and 7.26.
