  Using a new sample of extremely metal poor systems, the EMPRESS survey has
recently reported a primordial helium abundance that is $3\sigma$ smaller than
the prediction from the standard big bang nucleosynthesis (BBN) scenario. This
measurement could be interpreted as a hint for a primordial lepton asymmetry in
the electron neutrino flavor. Motivated by the EMPRESS results, we present a
comprehensive analysis of the lepton asymmetry using measurements of the
abundances of primordial elements, along with cosmic microwave background (CMB)
data from Planck. Assuming that there is no dark radiation in our Universe, we
find an electron neutrino chemical potential $\xi_{\nu_e} = 0.043 \pm 0.015$,
which deviates from zero by $2.9\sigma$. If no assumption is made on the
abundance of dark radiation in the Universe, the chemical potential is
$\xi_{\nu_e} = 0.046 \pm 0.021$, which deviates from zero by $2.2\sigma$. We
also find that this result is rather insensitive to the choice of nuclear
reaction rates. If the true helium abundance corresponds to the EMPRESS central
value, future CMB observations from the Simons Observatory and CMB-S4 will
increase the significance for a nonzero lepton asymmetry to $4\sigma$ and
$5\sigma$ respectively, assuming no dark radiation, or to $3\sigma$ when no
assumption is made on the abundance of dark radiation.
