The extreme astrophysical processes and conditions that characterise the early Universe are expected to result in young galaxies that are dynamically different from those observed today. This is because the strong effects associated with galaxy mergers and supernova explosions should lead to the majority of young star-forming galaxies being dynamically hot, chaotic and strongly unstable. With this presentation, I will show the discovery of a dynamically cold, but highly star-forming, rotating disk in a gravitationally lensed galaxy at redshift 4.2, when the Universe was just 1.4 billion years old. This galaxy is a typical dusty starburst, with global star-forming properties in agreement with current numerical simulations and observations of its galaxy population. However, ALMA interferometric imaging at a unique spatial resolution of 60 pc reveals a surprising ratio of rotational-to-random motions of V /σ = 9.7 ± 0.4, which is at least four times larger than expected from any galaxy evolution model at this epoch, but similar to spiral galaxies in the local Universe. This result requires galaxy evolution models to produce dynamically cold galaxies, not characterised by large turbulent motions and violent instabilities, already at early times. The rotation curve of this galaxy demonstrates that at at least some young galaxies are dynamically akin to those observed in the local Universe, and only weakly affected by extreme physical processes. Finally, I will show the preliminary results obtained by studying the dynamical properties of a sample of star-forming galaxies at z ~ 4–5.