Natural materials, such as bone and spider silk, possess remarkable properties as a result of sophisticated nanoscale structuring. They have inspired the design of synthetic materials whose structure at the nanoscale is carefully engineered or where nanoparticles, such as rods or wires, are self-assembled. Although much work has been done in recent years to create ordered structures using diblock copolymers and template-assisted assembly, no reports describe highly ordered, three-dimensional nanotube arrays within a polymeric material. There are only reports of two-dimensional network structures and structures on micrometer-size scales. Here, we describe an approach that uses plasticized colloidal particles as a template for the self-assembly of carbon nanotubes (CNTs) into ordered, three-dimensional networks. The nanocomposites can be strained by over 200% and still retain high conductivity when relaxed. The method is potentially general and so may find applications in areas such as sensing, photonics, and functional composites.