The Breakthrough Starshot research program envisions a laser-propelled sail that will probe our neighboring stars within a human lifetime. Starshot spacecraft weigh no more than a few grams and are accelerated by photon momentum transfer with a beam generated by a kilometer-scale, ground-based 100 GW coherent phased-array laser. We describe some of the major challenges for the laser and early exploratory efforts to overcome them. While challenges remain, we find no physical or economic restrictions that would preclude such a laser for the Starshot mission.