The wavelength of the 3s(1/2)-3p(3/2) transition of Na-like U81+ was determined to be 9.499 85+/-0.000 15 Angstrom (1305.12+/-0.02 eV), using the EBIT-I electron beam ion trap. The measurement is many times more sensitive to the radiative contributions from quantum electrodynamics than earlier measurements for Pt67+ and Pb71+. Our result strongly deviates from various predictions employing scaled hydrogenic quantum electrodynamic corrections and establishes a benchmark for multielectron QED calculations that agrees well with the trend established by ab initio calculations.