  This Letter presents a new, remarkably simple diagnostic specifically
designed to derive chemical abundances for high redshift galaxies. It uses only
the H \alpha, [N II] and [S II] emission lines, which can usually be observed
in a single gating stetting, and is almost linear up to an abundance of 12+log
(O/H) = 9.05. It can be used over the full abundance range encountered in high
redshift galaxies. By its use of emission lines located close together in
wavelength, it is also independent of reddening. Our diagnostic depends
critically on the calibration of the N/O ratio. However, by using realistic
stellar atmospheres combined with the N/O vs. O/H abundance calibration derived
locally from stars and H II regions, and allowing for the fact that
high-redshift H II regions have both high ionisation parameters \emph{and} high
gas pressures, we find that the observations of high-redshift galaxies can be
simply explained by the models without having to invoke arbitrary changes in
N/O ratio, or the presence of unusual quantities of Wolf-Rayet stars in these
galaxies.
