Due to the nature of their implementation, nearly all low-level fabrication processes produce solidly filled structures. However, lattice structures are significantly stronger for the same amount of material, resulting in structures that are much lighter and more materially efficient. In this paper we propose an approach for fabricating lattice structures that echoes commercially successful additive manufacturing/3D printing techniques. In it, a modular chain of specially designed links is “extruded” onto a substrate to produce various lattice configurations depending on the chosen assembly algorithm, ranging from one of the strongest known rigid lattices, the octet-truss, to significantly less dense configurations. Like 3D printing, the process allows material to be compactly stored before being deployed into structures of nearly arbitrary geometry, but unlike it, the approach allows for the use of nearly any material or combination of materials. We demonstrate the concept experimentally with a nearly 300-link chain that is fed from a spool and autonomously laid down onto programmed lattice arrangements via a robotic arm modified for the task. In the current prototype implementation, ~300-link structures are fabricated in 27 minutes, and a 3x3x2 lattice structure (287 total links) is shown to support approximately 1000N in compression testing.