The contact phase expected to precede the coalescence of two massive stars is poorly characterized due to the paucity of observational constraints. Here we report on the discovery of VFTS 352, an O-type binary in the 30 Doradus region, as the most massive and earliest spectral type overcontact system known to date. We derived the 3D geometry of the system, its orbital period P-orb = 1.1241452(4) day, components' effective temperatures-T-1 = 42 540 +/- 280 K and T-2 = 41 120 +/- 290 K-and dynamical masses-M-1 = 28.63 +/- 0.30 M-circle dot and M-2= 28.85 +/- 0.30 M-circle dot. Compared to single-star evolutionary models, the VFTS 352 components are too hot for their dynamical masses by about 2700 and 1100 K, respectively. These results can be explained naturally as a result of enhanced mixing, theoretically predicted to occur in very short-period tidally locked systems. The VFTS 352 components are two of the best candidates identified so far to undergo this so-called chemically homogeneous evolution. The future of VFTS 352 is uncertain. If the two stars merge, a very rapidly rotating star will be produced. Instead, if the stars continue to evolve homogeneously and keep shrinking within their Roche Lobes, coalescence can be avoided. In this case, tides may counteract the spin down by winds such that the VFTS 352 components may, at the end of their life, fulfill the requirements for long gamma-ray burst (GRB) progenitors in the collapsar scenario. Independently of whether the VFTS 352 components become GRB progenitors, this scenario makes VFTS 352 interesting as a progenitor of a black hole binary, hence as a potential gravitational wave source through black hole-black hole merger.