We study the influence of lepton asymmetry on the evolution of the early Universe. The lepton asymmetry l is poorly constrained by observations and might be orders of magnitude larger than the baryon asymmetry b, |l|/b 2 × 108. We find that lepton asymmetries that are large compared to the tiny baryon asymmetry, can influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the μB − T phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. Large lepton asymmetry could lead to a cosmic QCD phase transition of first order.