  We derive expression for the large b_perp asymptotic of the 3D parton
distributions q(x,b_perp) in the pion. The asymptotic depends exclusively on
the mass scales F_pi and m_pi. Therefore it provides us with a nice example of
a strict non-perturbative result for the partonic structure of Nambu-Goldstone
bosons in QCD. Analyzing the x-dependent pion transverse radius we reveal a new
phenomenon of "chiral inflation"-- in the parametrically wide region of Bjorken
x (m_pi^2/(4 pi F_pi)^2 << x << 1) the pion radius grows exponentially fast
with the rapidity eta=ln(1/x). We show that the partons in this interval of
Bjorken x contribute to famous logarithmic divergency of the pion radius. In
other words, the partonic picture of the classical result of ChPT is provided.
The phenomenon of the chiral inflation is at variance with the Gribov
diffusion, because of long-range interaction of the Nambu-Goldstone bosons.
