A new measurement of the cosmic-ray antiproton-to-proton flux ratio between 1 and 100 GeV is presented. The results were obtained with the PAMELA experiment, which was launched into low-Earth orbit on-board the Resurs-DK1 satellite on June 15th 2006. During 500 days of data collection a total of about 1000 antiprotons have been identified, including 100 above an energy of 20 GeV. The high-energy results are a tenfold improvement in statistics with respect to all previously published data. The data follow the trend expected from secondary production calculations and significantly constrain contributions from exotic sources, e.g., dark matter particle annihilations.