  A cosmic lepton asymmetry
$\eta_{\text{l}}=(n_{\text{l}}-n_{\bar{\text{l}}})/n_{\gamma}$ affects the
primordial helium abundance and the expansion rate of the early Universe. Both
of these effects have an impact on the anisotropies of the cosmic microwave
background (CMB). We derive constraints on the neutrino chemical potentials
from the Planck 2015 data, assuming equal lepton flavour asymmetries and
negligible neutrino masses. We find $\xi=-0.002 ^{+0.114}_{-0.111}$ (95\% CL)
for the chemical potentials, which corresponds to $ -0.085 \leq \eta_{\text{l}}
\leq 0.084$. Our constraints on the lepton asymmetry are significantly stronger
than previous constraints from CMB data analysis and we argue that they are
more robust than those from primordial light element abundances. The resulting
constraints on the primordial helium and deuterium abundances are consistent
with those from direct measurements.
