  Using a soft pion theorem based on chiral symmetry and a $\Delta(1232)$
resonance model we propose an estimate for the production cross section of low
energy pions in the deeply virtual Compton scattering (DVCS) process. In
particular, we express the $e p \to e \gamma \pi N$ processes in terms of
generalized parton distributions. We provide estimates of the contamination of
the $e p \to e \gamma p$ DVCS observables due to this associated pion
production processes when the experimental data are not fully exclusive, for a
set of kinematical conditions representative of present or planned experiments
at JLab, HERMES and COMPASS.
