We present measurements of galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). These use the Data Release 9 (DR9) CMASS sample, which contains 264 283 massive galaxies covering 3275 square degrees with an effective redshift z = 0.57 and redshift range 0.43 < z < 0.7. Assuming a concordance ΛCDM cosmological model, this sample covers an effective volume of 2.2 Gpc3, and represents the largest sample of the Universe ever surveyed at this density, . We measure the angle-averaged galaxy correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of 5σ in both the correlation function and power spectrum. Combining with the SDSS-II luminous red galaxy sample, the detection significance increases to 6.7σ. Fitting for the position of the acoustic features measures the distance to z = 0.57 relative to the sound horizon DV/rs = 13.67 ± 0.22 at z = 0.57. Assuming a fiducial sound horizon of 153.19 Mpc, which matches cosmic microwave background constraints, this corresponds to a distance DV (z = 0.57) = 2094 ± 34 Mpc. At 1.7 per cent, this is the most precise distance constraint ever obtained from a galaxy survey. We place this result alongside previous BAO measurements in a cosmological distance ladder and find excellent agreement with the current supernova measurements. We use these distance measurements to constrain various cosmological models, finding continuing support for a flat Universe with a cosmological constant.