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We obtained 16 VLT/X-shooter observations of GX 339-4 in quiescence in theperiod May - September 2016 and detected absorption lines from the donor starin its NIR spectrum. This allows us to measure the radial velocity curve andprojected rotational velocity of the donor for the first time. We confirm the1.76 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$^{-1}$. Fromthese values we compute a mass function $f(M) =1.91 \pm 0.08~M_{\odot}$, afactor $\sim 3$ lower than previously reported, and a mass ratio $q = 0.18 \pm0.05$. 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 binaryinclination 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 thefirst black hole to fall in the 'mass-gap' of $2-5~M_{\odot}$.

The mass function of GX 339-4 from spectroscopic observations of its donor star