A tunable, pulsed laser was used to excite the Lyman-α transition (1S–2P) of positronium (Ps). The laser system has a large bandwidth of GHz at nm, providing significant coverage of the Doppler-broadened, single-photon transition. The infra-red fundamental of a Nd:YAG laser was converted to ultraviolet by a series of solid-state, nonlinear processes, centred about an unseeded optical parametric oscillator, from which the bulk of the ultimate bandwidth derives. The Ps atoms were created by bombarding mesoporous silica with positrons, and the Doppler-width of the 1S–2P transition of the resulting ensemble was measured to be GHz (equivalent to K). It is envisaged that the UV laser will be incorporated into a two-step process to efficiently form Rydberg states of Ps, with potential applications in synthesis of cold antihydrogen, gravity measurements with antimatter, or for injection of electrons and positrons into a stellarator.