The lithium–sulfur battery is receiving intense interest because its theoretical energy density exceeds that of lithium-ion batteries at much lower cost, but practical applications are still hindered by capacity decay caused by the polysulfide shuttle. Here we report a strategy to entrap polysulfides in the cathode that relies on a chemical process, whereby a host—manganese dioxide nanosheets serve as the prototype—reacts with initially formed lithium polysulfides to form surface-bound intermediates. These function as a redox shuttle to catenate and bind ‘higher’ polysulfides, and convert them on reduction to insoluble lithium sulfide via disproportionation. The sulfur/manganese dioxide nanosheet composite with 75 wt% sulfur exhibits a reversible capacity of 1,300 mA h g⁻¹ at moderate rates and a fade rate over 2,000 cycles of 0.036%/cycle, among the best reported to date. We furthermore show that this mechanism extends to graphene oxide and suggest it can be employed more widely.