  We estimate the sizeable cross section for deep exclusive electroproduction
of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production
amplitude scales like the one for usual meson electroproduction, i.e. as
$1/Q^2$. This is due to the non-vanishing leading twist distribution amplitude
for the hybrid meson, which may be normalized thanks to its relation to the
energy momentum tensor and to the QCD sum rules technique. The hard amplitude
is considered up to next-to-leading order in $\alpha_{S}$ and we explore the
consequences of fixing the renormalization scale ambiguity through the BLM
procedure. We study the particular case where the hybrid meson decays through a
$\pi\eta $ meson pair. We discuss the $\pi\eta$ generalized distribution
amplitude and then calculate the production amplitude for this process. We
propose a forward-backward asymmetry in the production of $\pi$ and $\eta$
mesons as a signal for the hybrid meson production. We briefly comment on
hybrid electroproduction at very high energy, in the diffractive limit where a
QCD Odderon exchange mechanism should dominate. The conclusion of our study is
that hard electroproduction is a promissing way to study exotic hybrid mesons,
in particular at JLAB, HERA (HERMES) or CERN (Compass).
