It has been known for many years that the first excited state of 229Th lies close to the ground state. Originally this energy was given as <0.1 keV; later, the authors reported a value of -1+/-4 eV. In an attempt to improve the value for this level energy, we have remeasured the energies of a number of γ rays from 223U whose positions in the 229Th level scheme can be used to establish it. Compared with our earlier study, we have considered more γ rays in 229Th, used more well-measured energy calibration and reference lines, used more detectors, used detectors with better low-energy resolution, more closely matched the counting rates in the γ-ray peaks whose relative energy is measured, and specifically considered certain systematic errors. More than 111 γ-ray spectra have been measured. From this large set of measurements we have deduced a value of 3.5+/-1.0 eV for the energy of this level.