  Chiral perturbation theory (ChPT) is a low-energy effective field theory of
QCD and also a nonlinear sigma model based on the symmetry breaking pattern
${\rm SU}(N_f)\times {\rm SU}(N_f)\to {\rm SU}(N_f)$. In the limit of massless
$N_f$ quarks, we enumerate the independent operators without external sources
in ChPT using an on-shell method, by counting and presenting the soft blocks at
each order in the derivative expansion, up to ${\cal O}(p^{10})$. Given the
massless on-shell condition and total momentum conservation, soft blocks are
homogeneous polynomials of kinematic invariants exhibiting the Adler's zero
when any external momentum becomes soft and vanishing. In addition, soft blocks
are seeds for recursively generating all tree amplitudes of Nambu-Goldstone
bosons without recourse to ChPT, and in one-to-one correspondence with the "low
energy constants" which are the Wilson coefficients. Relations among operators,
such as those arising from equations of motion, integration-by-parts,
hermiticity, and symmetry structure, manifest themselves in the soft blocks in
simple ways. We find agreements with the existing results up to NNNLO, and make
a prediction at N$^4$LO.
