The pathway to forming the iron-rich planet Mercury remains mysterious. Its core makes up 70% of the planetary mass, which implies a significant enrichment of iron relative to silicates, while its mantle is strongly depleted in oxidised iron. The high core mass fraction is traditionally ascribed to evaporative loss of silicates, for example following a giant impact, but the high abundance of moderately volatile elements in the mantle of Mercury is inconsistent with reaching temperatures significantly above 1000 K during its formation. Here we explore the nucleation of solid particles from a gas of solar composition that cools down in the hot inner regions of the protoplanetary disc. The high surface tension of iron causes iron particles to nucleate homogeneously (i.e. not on a more refractory substrate) under very high supersaturation. The low nucleation rates lead to depositional growth of large iron pebbles on a sparse population of nucleated iron nanoparticles. Silicates in the form of iron-free MgSiO3 nucleate at similar temperatures but obtain smaller sizes because of the much higher number of nucleated particles. This results in a chemical separation of large iron particles from silicate particles with ten times lower Stokes numbers. We propose that such conditions lead to the formation of iron-rich planetesimals by the streaming instability. In this view, Mercury formed by accretion of iron-rich planetesimals with a subsolar abundance of highly reduced silicate material. Our results imply that the iron-rich planets known to orbit the Sun and other stars are not required to have experienced mantle-stripping impacts. Instead, their formation could be a direct consequence of temperature fluctuations in protoplanetary discs and chemical separation of distinct crystal species through the ensuing nucleation process.