  We have measured a strong increase of the low-temperature resistivity
$\rho_{xx}$ and a zero-value plateau in the Hall conductivity $\sigma_{xy}$ at
the charge neutrality point in graphene subjected to high magnetic fields up to
30 T. We explain our results by a simple model involving a field dependent
splitting of the lowest Landau level of the order of a few Kelvin, as extracted
from activated transport measurements. The model reproduces both the increase
in $\rho_{xx}$ and the anomalous $\nu=0$ plateau in $\sigma_{xy}$ in terms of
coexisting electrons and holes in the same spin-split zero-energy Landau level.
