  We present a calculation of valence double parton distributions of the pion
in the framework of chiral quark models. The result obtained at the low-energy
quark model scale is particularly simple, where in the chiral limit a
factorized form follows, $D(x_1,x_2, \vec{q}) = \delta(1-x_1-x_2) F(\vec{q})$
with $x_{1,2}$ standing for the longitudinal momentum fractions of the valence
quark and antiquark, and $\vec{q}$ denotes the relative transverse momentum.
For $\vec{q}=\vec{0}$ the result satisfies the Gaunt-Sterling sum rules. The
QCD evolution to higher scales is carried out within the dDGLAP framework. We
argue that the ratios of the valence Mellin moments $\langle x_1^n x_2^m
\rangle / \langle x_1^n \rangle \langle x_2^m \rangle $, which do not depend on
the dDGLAP evolution, provide particularly convenient measures of the
longitudinal correlations between the partons. Such ratios could be probed in
future lattice QCD simulations.
