  We present spectral and timing analysis of NuSTAR observations of RX
J0520.5$-$6932 in the 3-79 keV band collected during its outburst in January
2014. The target was observed on two epochs and we report the detection of a
cyclotron resonant scattering feature with central energies of $E_\mathrm{CRSF}
= 31.3_{-0.7}^{+0.8}$ keV and $31.5_{-0.6}^{+0.7}$ keV during the two
observations, respectively, corresponding to a magnetic field of $B \approx 2
\times10^{12}$ G. The 3-79 keV luminosity of the system during the two epochs
assuming a nominal distance of 50 kpc was $3.667\pm0.007\times
10^{38}\,\mathrm{erg\,s^{-1}}$ and
$3.983\pm0.007\times10^{38}\,\mathrm{erg\,s^{-1}}$. Both values are much higher
than the critical luminosity of $\approx1.5\times10^{37}\,\mathrm{erg\,s^{-1}}$
above which a radiation dominated shock front may be expected. This adds a new
object to the sparse set of three systems that have a cyclotron line observed
at luminosities in excess of $10^{38}\,\mathrm{erg\,s^{-1}}$. A broad
($\sigma\approx0.45$ keV) Fe emission line is observed in the spectrum at a
central energy of $6.58_{-0.05}^{+0.05}$ keV in both epochs. The pulse profile
of the pulsar was observed to be highly asymmetric with a sharply rising and
slowly falling profile of the primary peak. We also observed minor variations
in the cyclotron line energy and width as a function of the rotation phase.% As
in observations of other cyclotron absorption line sources, there is a small
($\Delta\phi\lesssim0.1$) phase difference between the peak of the cyclotron
energy variation and the peak of the flux variation.
