Density functional theory calculations and crystal structure predictions using the particle swarm optimization method have been combined to determine stable hydrides of lead under pressure. In contrast to other group-IVa hydrides, the stoichiometry PbH6 is the first hydride to become stable, at just under 1 Mbar. For two previously studied stoichiometries PbH4 and PbH8, new energetically favorable phases were identified to become stable around 2 Mbar. In all structures, the hydrogenic sublattices comprises negatively charged H δ− 2 molecules. Competitive PbH4 and PbH6 structures are layered. PbH6 features H2 molecules intercalated between hexagonal close packed Pb-layers, the stable phase of dense pure lead, thus offering a potentially straightforward route towards synthesis. In PbH8, the Pb lattice adapts a beta-Sn structure and hydrogen atoms form quasi-1D-chains. All structures were found to be metallic and to feature superconductivity in their respective stability range, with moderately high Tc in the range 60-100 K for PbH4 and PbH6, and 161-178 K for PbH8.