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 +/- 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 ~ 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.
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