We report on the first measurement of the fission barrier height in a heavy shell-stabilized nucleus. The fission barrier height of No254 is measured to be Bf=6.0±0.5 MeV at spin 15 and, by extrapolation, Bf=6.6±0.9 MeV at spin 0. This information is deduced from the measured distribution of entry points in the excitation energy versus spin plane. The same measurement is performed for Th220 and only a lower limit of the fission barrier height can be determined: Bf(I)>8 MeV. Comparisons with theoretical fission barriers test theories that predict properties of superheavy elements
