We measure the imprint of baryon acoustic oscillations ( BAOs ) in the galaxy clustering pattern at the highest redshift achieved to date , z = 0.6 , using the distribution of N = 132 { , } 509 emission-line galaxies in the WiggleZ Dark Energy Survey . We quantify BAOs using three statistics : the galaxy correlation function , power spectrum and the band-filtered estimator introduced by Xu et al . ( 2010 ) . The results are mutually consistent , corresponding to a 4.0 \% measurement of the cosmic distance-redshift relation at z = 0.6 ( in terms of the acoustic parameter “ A ( z ) ” introduced by Eisenstein et al . ( 2005 ) we find A ( z = 0.6 ) = 0.452 \pm 0.018 ) . Both BAOs and power spectrum shape information contribute toward these constraints . The statistical significance of the detection of the acoustic peak in the correlation function , relative to a wiggle-free model , is 3.2 - \sigma . The ratios of our distance measurements to those obtained using BAOs in the distribution of Luminous Red Galaxies at redshifts z = 0.2 and z = 0.35 are consistent with a flat \Lambda Cold Dark Matter model that also provides a good fit to the pattern of observed fluctuations in the Cosmic Microwave Background ( CMB ) radiation . The addition of the current WiggleZ data results in a \approx 30 \% improvement in the measurement accuracy of a constant equation-of-state , w , using BAO data alone . Based solely on geometric BAO distance ratios , accelerating expansion ( w < -1 / 3 ) is required with a probability of 99.8 \% , providing a consistency check of conclusions based on supernovae observations . Further improvements in cosmological constraints will result when the WiggleZ Survey dataset is complete .