Quasiparticle interactions broaden spectral features at surfaces, which can be measured using the scanning tunneling microscope (STM). We report the first study of lifetime effects on Shockley surface-state electrons using low-temperature STM spectroscopy. Data taken from Ag(111) are analyzed using detailed tunneling calculations and a simple model, and are found to correspond to a self-energy of Σ = 4.9±0.6meV. This is considerably below values determined by angle-resolved photoemission, but remains higher than theoretical predictions.