We demonstrate the first application of reconstruction to a galaxy redshift survey using the observed galaxies in the SDSS DR7 luminous red galaxy catalogue. Our reconstruction procedure is analogous to running gravity backwards and aids in obtaining a more precise measurement of the acoustic scale. We validate our reconstruction, covariance matrix and fitting techniques on 160 mock catalogues derived from the LasDamas simulations in redshift space. We then apply these techniques to the DR7 LRG sample and find that the error on the acoustic scale decreases from ~3.5% before reconstruction to ~1.9% after reconstruction. This factor of 1.8 reduction in the error is equivalent to the effect of increasing the survey volume by about a factor of 3. We also see an increase by at least 1-sigma in the significance of our BAO detection for 2 different measures of BAO significance. Using our distance measure to constrain cosmology, we find our data is consistent with a standard LCDM universe. However, our data may show slight hints that the number of relativistic neutrino species is higher than currently thought.