We report heat transport measurements in a cylindrical convection apparatus rotating about the vertical axis. The aspect ratio was 1/2. The working fluid was cryogenic helium gas and the following parameter ranges applied: the Rayleigh number, Ra, varied in the range 10(11) < Ra < 4.3 x 10(15), the Taylor number, Ta, varied in the range 10(11) < Ta < 3 x 10(15), the convective Rossby number, Ro, varied in the range 0.4 < Ro < 1.6 and the Prandtl number, Pr, varied in the range 0.7 < Pr < 5.9. Boussinesq conditions applied quite closely. The heat transport for steady rotation, under all conditions of the present experiments, was smaller than that for the non-rotating case. When the rotation rate varied periodically in time, a sharp transition to a state of significantly enhanced heat transport was observed for modulation Taylor numbers Ta* greater than or similar to 10(14), where Ta* is based on the peak value of the modulation angular velocity.