Although electrons and photons are intrinsically different, importing useful concepts in optics to electronics performing similar functions has been actively pursued over the last two decades. In particular, collimation of an electron beam is a long-standing goal. We show that ballistic propagation of an electron beam with virtual no spatial spreading or diffraction, without a waveguide or external magnetic field, can be achieved in graphene under an appropriate class of experimentally feasible one-dimensional external periodic potentials. The novel chiral quasi-one-dimensional metallic state that the charge carriers are in originates from a collapse of the intrinsic helical nature of the charge carriers in graphene owing to the superlattice potential. Beyond providing a new way to constructing chiral one-dimensional states in two dimensions, our findings should be useful in graphene-based electronic devices (e.g., for information processing) utilizing some of the highly developed concepts in optics.