The lepton avour asymmetries of the Universe are observationally almost unconstrained before
the onset of neutrino oscillations. We calculate the cosmic trajectory during the cosmic QCD epoch
in presence of large lepton avour asymmetries. By including QCD thermodynamic quantities
derived from functional QCD methods into our calculation our work reveals for the rst time the
possibility of a rst-order cosmic QCD transition. We specify the required values of the lepton
avour asymmetries for which a rst-order transition occurs for a number of di erent benchmark
scenarios.