In order for the widely discussed benefits of flow batteries for electrochemical energy storage to be applied at large scale, the cost of the electrochemical stack must come down substantially. One promising avenue for reducing stack cost is to increase the system power density while maintaining efficiency, enabling smaller stacks. Here we report on a membrane-less, hydrogen bromine laminar flow battery as a potential high power density solution. The membrane-less design enables power densities of 0.795 W cm$^{-2}$ at room temperature and atmospheric pressure, with a round-trip voltage efficiency of 92% at 25% of peak power. Theoretical solutions are also presented to guide the design of future laminar flow batteries. The high power density achieved by the hydrogen bromine laminar flow battery, along with the potential for rechargeable operation, will translate into smaller, inexpensive systems that could revolutionize the fields of large-scale energy storage and portable power systems.