The ability to store energy on the electric grid would greatly improve its efficiency and reliability while enabling the integration of intermittent renewable energy technologies (such as wind and solar) into baseload supply. Batteries have long been considered strong candidate solutions owing to their small spatial footprint, mechanical simplicity and flexibility in siting. However, the barrier to widespread adoption of batteries is their high cost. Here we describe a lithium-antimony-lead liquid metal battery that potentially meets the performance specifications for stationary energy storage applications. This Li||Sb-Pb battery comprises a liquid lithium negative electrode, a molten salt electrolyte, and a liquid antimony-lead alloy positive electrode, which self-segregate by density into three distinct layers owing to the immiscibility of the contiguous salt and metal phases. The all-liquid construction confers the advantages of higher current density, longer cycle life and simpler manufacturing of large-scale storage systems (because no membranes or separators are involved) relative to those of conventional batteries. At charge-discharge current densities of 275 milliamperes per square centimetre, the cells cycled at 450 degrees Celsius with 98 per cent Coulombic efficiency and 73 per cent round-trip energy efficiency. To provide evidence of their high power capability, the cells were discharged and charged at current densities as high as 1,000 milliamperes per square centimetre. Measured capacity loss after operation for 1,800 hours (more than 450 charge-discharge cycles at 100 per cent depth of discharge) projects retention of over 85 per cent of initial capacity after ten years of daily cycling. Our results demonstrate that alloying a high-melting-point, high-voltage metal (antimony) with a low-melting-point, low-cost metal (lead) advantageously decreases the operating temperature while maintaining a high cell voltage. Apart from the fact that this finding puts us on a desirable cost trajectory, this approach may well be more broadly applicable to other battery chemistries.