Hot Jupiters are giant Jupiter-like exoplanets that orbit 100x closer to their host stars than Jupiter does to the Sun. These planets presumably form in the outer part of the primordial disc from which both the central star and surrounding planets are born, then migrate inwards and yet avoid falling into their host star. It is however unclear whether this occurs early in the lives of hot Jupiters, when still embedded within protoplanetary discs, or later, once multiple planets are formed and interact. Although numerous hot Jupiters were detected around mature Sun-like stars, their existence has not yet been firmly demonstrated for young stars, whose magnetic activity is so intense that it overshadows the radial velocity signal that close-in giant planets can induce. Here we show that hot Jupiters around young stars can be revealed from extended sets of high-resolution spectra. Once filtered-out from the activity, radial velocities of V830 Tau derived from new data collected in late 2015 exhibit a sine wave of period 4.93 d and semi-amplitude 75 m/ s, detected with a false alarm probability <0.03%. We find that this signal is fully unrelated to the 2.741-d rotation period of V830 Tau and we attribute it to the presence of a 0.77 Jupiter mass planet orbiting at a distance of 0.057 au from the host star. Our result demonstrates that hot Jupiters can migrate inwards in <2 Myr, most likely as a result of planet-disc interactions, and thus yields strong support to the theory of giant planet migration in gaseous protoplanetary discs.