  Within a chiral quark model, we evaluate the good cross section in the
Euclidean space in the vector - axial vector channel, proposed recently by Ma
and Qiu as means to extract the so far elusive parton distribution functions of
the pion from lattice QCD. Our results are remarkably simple at the quark model
scale and agree well, after the necessary QCD evolution, with with the most
recent lattice calculations at the scale $\mu \sim 2$ GeV for various values of
the lattice pion mass. Comparisons are made as functions of the Ioffe time
variable. We also comment on the information on the lowest moments in the
momentum fraction $x$, generically extractable from such analyses, as well as
on the inaccessibility of the $x \to 1$ limit from the present data.
