Measurement of the Spin-Orbit Alignment in the Exoplanetary System HD 189733

We present spectroscopy of a transit of the exoplanet HD 189733b. By modeling the Rossiter-McLaughlin effect (the anomalous Doppler shift due to the partial eclipse of the rotating stellar surface), we find the angle between the sky projections of the stellar spin axis and orbit normal to be lambda = -1.4 +/- 1.1 deg. This is the third case of a ``hot Jupiter'' for which lambda has been measured. In all three cases lambda is small, ruling out random orientations with 99.96% confidence, and suggesting that the inward migration of hot Jupiters generally preserves spin-orbit alignment.