This paper reports on the first demonstration of electron Bernsteinwave heating (EBWH) by double mode conversion from ordinary (O-) to Bernstein (B-) via the extraordinary (X-) mode in an over-dense tokamak plasma, using low field side launch, achieved in the TCV tokamak H-mode, making use of its naturally generated steep density gradient. This technique offers the possibility of overcoming the upper density limit of conventional EC microwave heating. The sensitive dependence of the O-X mode conversion on the microwave launching direction has been verified experimentally. Localized power deposition, consistent with theoretical predictions, has been observed at densities well above the conventional cut-off. Central heating has been achieved, at powers up to two megawatts. This demonstrates the potential of EBW in tokamak H-modes, the intended mode of operation for a reactor such as ITER.