  We investigate neutral pion electroproduction off protons in the framework of
heavy baryon chiral perturbation theory. The chiral expansion of the S--wave
multipoles $E_{0+}$ and $L_{0+}$ is carried out to three orders. There appear
several undetermined low--energy constants. Three are taken from a recent study
of the new TAPS threshold $\pi^0$ photoproduction data, one is fixed from the
proton Dirac form factor and the novel S--wave constants appearing at orders
$q^4$ and $q^5$ are determined from a best fit (constrained by resonance
exchange) to the recent NIKHEF and MAMI data at photon momentum transfer
squared $k^2 = -0.1 \, \, {\rm GeV}^2$. The inclusion of a particular set of
dimension five operators is forced upon the fit by a soft--pion theorem which
severely constrains the momentum dependence of the longitudinal S--wave
multipole $L_{0+}$ at order $q^4$. We give predictions for lower photon
virtualities for the various multipoles and differential cross sections.
Further improvements are briefly touched upon.
