The baryon acoustic oscillations are a promising route to the precisionmeasure of the cosmological distance scale and hence the measurement ofthe time evolution of dark energy. We show that the nonlineardegradation of the acoustic signature in the correlations oflow-redshift galaxies is a correctable process. By suitablereconstruction of the linear density field, one can sharpen the acousticpeak in the correlation function or, equivalently, restore the higherharmonics of the oscillations in the power spectrum. With this, one canachieve better measurements of the acoustic scale for a given surveyvolume. Reconstruction is particularly effective at low redshift, wherethe nonlinearities are worse but where the dark energy density ishighest. At z=0.3, we find that one can reduce the sample variance errorbar on the acoustic scale by at least a factor of 2 and in principle bynearly a factor of 4. We discuss the significant implications ourresults have for the design of galaxy surveys aimed at measuring thedistance scale through the acoustic peak.