Building an evolvable physical self-replicating machine is a grand challenge. The main problem is that the device must be capable of hereditary variation, that is, replicating in many configurations—configurations into which it enters unpredictably by mutation. Template replication is the solution found by nature. A scalable device must also be capable of miniaturization, and so have few or no moving and electronic parts. Here a significant step toward this goal is presented in the form of a physical template replicator made from small plastic pieces containing embedded magnets that float on an air-hockey-type table and undergo stochastic motion. Our units replicate by a process analogous to the replication of DNA, except without the involvement of enzymes. Building a physical rather than a computational model forces us to confront several problems that have analogues on the nano scale. In particular, replication must be maintained by preventing side reactions such as spontaneous ligation, cyclization, product inhibition, and elongation at staggered ends. The last of these results in ever-lengthening sequences in a process known as the elongation catastrophe. The extreme specificity of structure required by the monomers is indirect evidence that some kind of natural selection took place prior to the existence of nucleotide analogues during the origin of life.