Excellent energy resolution is one of the primary advantages of electroluminescent high pressure xenon TPCs, and searches for rare physics events such as neutrinoless double-beta decay ($betabeta0 u$) require precise energy measurements. Using the NEXT-White detector, developed by the NEXT (Neutrino Experiment with a Xenon TPC) collaboration, we show for the first time that an energy resolution of 1% FWHM can be achieved at 2.6 MeV, establishing the present technology as the one with the best energy resolution of all xenon detectors for $betabeta0 u$ searches.