  We present the first spectroscopic measurement of multiple rest-frame optical
emission lines at $z>4$. During the MOSFIRE Deep Evolution Field (MOSDEF)
survey, we observed the galaxy GOODSN-17940 with the Keck I/MOSFIRE
spectrograph. The K-band spectrum of GOODSN-17940 includes significant
detections of the [OII]$\lambda\lambda 3726,3729$, [NeIII]$\lambda3869$, and
H$\gamma$ emission lines and a tentative detection of H$\delta$, indicating
$z_{\rm{spec}}=4.4121$. GOODSN-17940 is an actively star-forming $z>4$ galaxy
based on its K-band spectrum and broadband spectral energy distribution. A
significant excess relative to the surrounding continuum is present in the
Spitzer/IRAC channel 1 photometry of GOODSN-17940, due primarily to strong
H$\alpha$ emission with a rest-frame equivalent width of
$\mbox{EW(H}\alpha)=1200$ \AA. Based on the assumption of $0.5 Z_{\odot}$
models and the Calzetti attenuation curve, GOODSN-17940 is characterized by
$M_*=5.0^{+4.3}_{-0.2}\times 10^9 M_{\odot}$. The Balmer decrement inferred
from H$\alpha$/H$\gamma$ is used to dust correct the H$\alpha$ emission,
yielding $\mbox{SFR(H}\alpha)=320^{+190}_{-140} M_{\odot}\mbox{ yr}^{-1}$.
These $M_*$ and SFR values place GOODSN-17940 an order of magnitude in SFR
above the $z\sim 4$ star-forming "main sequence." Finally, we use the observed
ratio of [NeIII]/[OII] to estimate the nebular oxygen abundance in
GOODSN-17940, finding $\mbox{O/H}\sim 0.2 \mbox{ (O/H)}_{\odot}$. Combining our
new [NeIII]/[OII] measurement with those from stacked spectra at $z\sim 0, 2,
\mbox{ and } 3$, we show that GOODSN-17940 represents an extension to $z>4$ of
the evolution towards higher [NeIII]/[OII] (i.e., lower $\mbox{O/H}$) at fixed
stellar mass. It will be possible to perform the measurements presented here
out to $z\sim 10$ using the James Webb Space Telescope.
