We compare the properties of dwarf galaxies in the Local Group with the simulated galaxies formed before reionization in a cosmological simulation of unprecedented spatial and mass resolution including radiative feedback effects. We find that a subset of the Local Group dwarfs, the dwarf Spheroidals, are remarkably similar to the simulated dwarf galaxies in all their properties already before reionization. Simulated and observed dwarf Spheroidal galaxies not only have similar properties but also follow the same scaling relations. Based on this similarity and on the observed ages of their dominant stellar populations we propose the hypothesis that Local Group dwarfs form in two different ways: (i) most dwarf Spheroidals are pristine fossils of the pre-reionization era and (ii) dwarf irregulars are more massive galaxies that formed most of their stars later, after reionization. There is also a group of “polluted fossils” with properties that are intermediate between these two main groups. We predict the existence of many more dwarf Spheroidals, fainter and with lower surface brightness than the observed population.