The recently discovered homologous series HgBa(2)Can-1 Cun O2n+2+delta possesses remarkable properties. A superconducting transition temperature, T(c), as high as 133 kelvin has been measured in a multiphase Hg-Ba-Ca-Cu-O sample and found to be attributable to the Hg-1223 compound. Temperature-dependent electrical resistivity measurements under pressure on a (> 95%) pure Hg-1223 phase are reported. These data show that T(c) increases steadily with pressure at a rate of about 1 kelvin per gigapascal up to 15 gigapascals, then more slowly and reaches a T(c) = 150 kelvin, with the onset of the transition at 157 kelvin, for 23.5 gigapascals. This large pressure variation (as compared to the small effects observed in similar compounds with the optimal T(c)) strongly suggests that higher critical temperatures could be obtained at atmospheric pressure.