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, energetically more favorable phases were identified to become stable around 2 Mbar. In all structures, the hydrogenic sublattices comprise negatively charged H2δ− molecules. Competitive PbH4 and PbH6 structures are layered. PbH6 features H2 molecules intercalated between hcp Pb layers, the stable phase of dense pure lead, thus offering a potentially straightforward route towards synthesis. In PbH8, the Pb lattice adapts a β-Sn structure, and hydrogen atoms form quasi-one-dimensional-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.