Nanostructured devices have the potential to serve as the basis for next-generation energy systems that make use of densely packed interfaces and thin films. One approach to making such devices is to build multilayer structures of large area inside the open volume of a nanostructured template. Here, we report the use of atomic layer deposition to fabricate arrays of metal-insulator-metal nanocapacitors in anodic aluminium oxide nanopores. These highly regular arrays have a capacitance per unit planar area of approximately 10 microF cm-2 for 1-microm-thick anodic aluminium oxide and approximately 100 microF cm-2 for 10-microm-thick anodic aluminium oxide, significantly exceeding previously reported values for metal-insulator-metal capacitors in porous templates. It should be possible to scale devices fabricated with this approach to make viable energy storage systems that provide both high energy density and high power density.