  We report the detection of a black hole (NGC 1850 BH1) in the $\sim$100
Myr-old massive cluster NGC~1850 in the Large Magellanic Cloud. It is in a
binary system with a main-sequence turn-off star (4.9 $\pm$ 0.4 M${_\odot}$),
which is starting to fill its Roche Lobe and becoming distorted. Using 17
epochs of VLT/MUSE observations we detected radial velocity variations
exceeding 300 km/s associated to the target star, linked to the ellipsoidal
variations measured by OGLE-IV in the optical bands. Under the assumption of a
semi-detached system, the simultaneous modelling of radial velocity and light
curves constraints the orbital inclination of the binary to ($38 \pm
2$)$^{\circ}$, resulting in a true mass of the unseen companion of
$11.1_{-2.4}^{+2.1}$ $M_{\odot}$. This represents the first direct dynamical
detection of a black hole in a young massive cluster, opening up the
possibility of studying the initial mass function and the early dynamical
evolution of such compact objects in high-density environments.
