  We present the first application of the Basis Light-Front Quantization method
to study a simple chiral model of the nucleon-pion system via an ab initio,
non-perturbative, Hamiltonian approach. As a test problem, we consider the
physical proton as the relativistic bound state of the nucleon-pion system.
Based on the chiral model of the nucleon-pion system, we construct the
mass-squared matrix of the system within our light-front basis representation.
We obtain the proton's mass and the corresponding light-front wave function by
solving the eigenvalue problem of the mass-squared matrix. With the resulting
boost-invariant light-front wave function, we also compute the proton's parton
distribution function.
