A large neutrino asymmetry could have significant observable consequences for nucleosynthesis and the cosmic microwave background. If the baryon asymmetry originates via the Affleck-Dine mechanism along a d = 4 flat direction of the scalar potential in the minimal supersymmetric standard model and if the lepton asymmetry originates via Affleck-Dine leptogenesis along a d = 6 direction, corresponding to the lowest dimension directions conserving R parity, then the ratio nL/nB is naturally in the range 108–109. As a result, a potentially observable neutrino asymmetry is correlated with a baryon asymmetry of the order of 10-10.