  We present deeply virtual $\pi^0$ electroproduction cross-section
measurements at $x_B$=0.36 and three different $Q^2$--values ranging from 1.5
to 2 GeV$^2$, obtained from experiment E07-007 that ran in the Hall A at
Jefferson Lab. The Rosenbluth technique was used to separate the longitudinal
and transverse responses. Results demonstrate that the cross section is
dominated by its transverse component, and thus is far from the asymptotic
limit predicted by perturbative Quantum Chromodynamics. An indication of a
non-zero longitudinal contribution is provided by the interference term
$\sigma_{LT}$ also measured. Results are compared with several models based on
the leading twist approach of Generalized Parton Distributions (GPDs). In
particular, a fair agreement is obtained with models where the scattering
amplitude is described by a convolution of chiral-odd (transversity) GPDs of
the nucleon with the twist-3 pion distribution amplitude. Therefore, neutral
pion electroproduction may offer the exciting possibility of accessing
transversity GPDs through experiment.
