We study an extended QCD model in (1+1) dimensions obtained from QCD in 4D by compactifying two spatial dimensions and projecting onto the zero-mode subspace. We work out this model in the large N_c limit and using light cone gauge but keeping the equal-time quantization. This system is found to induce a dynamical mass for transverse gluons - adjoint scalars in QCD ₂, and to undergo a chiral symmetry breaking with the full quark propagators yielding non-tachyonic, dynamical quark masses, even in the chiral limit. We study quark-antiquark bound states which can be classified in this model by their properties under Lorentz transformations inherited from 4D. The scalar and pseudoscalar sectors of the theory are examined and in the chiral limit a massless ground state for pseudoscalars is revealed with a wave function generalizing the so called 't Hooft pion solution.