The first demonstration of electron-Bernstein-wave heating by double-mode conversion from the O to the X mode in an overdense H-mode tokamak plasma has been achieved in the Tokamak a` Configuration Variable device. This technique overcomes the upper density limit experienced by conventional microwave heating. The sensitive dependence of the O-X mode conversion on the microwave launching direction has been verified experimentally, and localized power deposition consistent with theoretical predictions has been observed at densities well above the conventional cutoff.