We compute the electrical conductivity for liquid hydrogen at high pressure using Monte Carlo techniques. The method uses coupled electron-ion Monte Carlo simulations to generate configurations of liquid hydrogen. For each configuration, correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give ac electrical conductivity. The extrapolated dc conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data.