Simultaneous current ramping and application of lower hybrid heating and current drive (LHCD) have produced a region with zero current density within measurement errors in the core ( r/a< or =0.2) of JET tokamak optimized shear discharges. The reduction of core current density is consistent with a simple physical explanation and numerical simulations of radial current diffusion including the effects of LHCD. However, the core current density is clamped at zero, indicating the existence of a physical mechanism which prevents it from becoming negative.