A new superconductor, Hg0.5Bi0.5Sr2-xLaxCuO5-delta with a T(c onset) of 27 K has been isolated for 0 less-than-or-equal-to x less-than-or-equal-to 0.75. This phase crystallizes in the tetragonal system with a almost-equal-to a(p) almost-equal-to 3.8 angstrom and c almost-equal-to 8.9 angstrom. Its X-ray diffraction and high resolution electron microscopy analysis show that it belongs, like the 94 K-superconductor HgBa2CuO4+delta, to the ''1201'' series. Its structure can be described as the intergrowth of single perovskite layers with double oxygen deficient rock salt layers built up from mixed layers [Hg0.5Bi0.5O1-delta]infinity. This unique ''Sr-Hg-1201'' cuprate opens the route to the exploration of ''mixed'' superconductors resulting from the substitution of mercury for different metallic cations such as Tl, Bi, Pb in the ''normal'' layers that ensure the junction between the superconducting copper layers.