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We demonstrate the laser excitation of the n=3 state of positronium (Ps) in vacuum. A combination of a specially designed pulsed slow positron beam and a high-efficiency converter target was used to produce Ps. Its annihilation was recorded by single-shot positronium annihilation lifetime spectroscopy. Pulsed laser excitation of the n=3 level at a wavelength λ≈205 nm was monitored via Ps photoionization induced by a second intense laser pulse at λ=1064 nm. About 15% of the overall positronium emitted into vacuum was excited to n=3 and photoionized. Saturation of both the n=3 excitation and the following photoionization was observed and explained by a simple rate equation model. The positronium's transverse temperature was extracted by measuring the width of the Doppler-broadened absorption line. Moreover, excitation to Rydberg states n=15 and 16 using n=3 as the intermediate level was observed, giving an independent confirmation of excitation to the 3P3 state.