  We obtained 16 VLT/X-shooter observations of GX 339-4 in quiescence in the
period May - September 2016 and detected absorption lines from the donor star
in its NIR spectrum. This allows us to measure the radial velocity curve and
projected rotational velocity of the donor for the first time. We confirm the
1.76 day orbital period and we find that $K_2$ = $219 \pm 3$ km s$^{-1}$,
$\gamma = 26 \pm 2$ km s$^{-1}$ and $v \sin i = 64 \pm 8$ km s$^{-1}$. From
these values we compute a mass function $f(M) =1.91 \pm 0.08~M_{\odot}$, a
factor $\sim 3$ lower than previously reported, and a mass ratio $q = 0.18 \pm
0.05$. We confirm the donor is a K-type star and estimate that it contributes
$\sim 45-50\%$ of the light in the $J$- and H-band. We constrain the binary
inclination to $37^\circ < i < 78^\circ$ and the black hole mass to
$2.3~M_{\odot} < M_\mathrm{BH} < 9.5~M_{\odot}$. GX 339-4 may therefore be the
first black hole to fall in the 'mass-gap' of $2-5~M_{\odot}$.
