A SPIN-1/2 Heisenberg antiferromagnetic ladder is a model system comprising parallel chains of interacting elemental spins. Spin ladders having an even number of chains have been predicted(1-6) to exhibit interesting dynamics, including superconductivity, when unoccupied spin sites are introduced along the chain (that is, when the chains are doped with holes). Spin-ladder models thus provide a novel potential mechanism for high-temperature superconductivity in real materials. But unfortunately materials with spin-ladder structure are quite rare(4-10), and the few known compounds have not previously been doped successfully with holes. Here we report the high-pressure synthesis of a new hole-doped two-chain ladder compound, La1-xSrxCuO2.5. We have observed a marked insulator-to-metal transition in this compound with increased doping, but no superconducting transition down to 5 K. The absence of superconductivity in this material must be reconciled with theoretical predictions based on ideal hole-doped spin-ladder models.