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In this paper, the concept of self-replicating robots (SRRs) is reviewed, and the feasibility of a particular kind of minimalistic SRR is analyzed in the context of lunar resource development. The key issue that will determine the feasibility of this approach is whether or not an autonomous robotic factory can be devised such that it is light enough to be transported to the moon, yet complete in its ability to self-replicate with no other inputs than those resources available on the lunar surface. Self-replication leads to exponential growth, and would allow as few as one initial factory to spawn lunar production of materials and energy on a massive scale. Such capacity would dramatically impact man's ability to explore and colonize space and collect solar energy for terrestrial applications. Our concept of a self-replicating robotic factory consists of four subsystems: 1) multifunctional robots for digging and transportation of materials, and assembly of components during the replication process; 2) materials refining and casting facility; 3) solar energy conversion, storage and transmission; and 4) electromagnetic rail guns for long-distance transportation (for example, for sending materials to low-earth orbit (LEO), or transporting replicated factories to distal points on the moon). Each of these subsystems is described in the context of current technologies, with an emphasis on 1). We build on previous concepts for self-replicating systems, present a simple prototype that demonstrates active mechanical replication, and develop an analytical model of how the proliferation of such systems on the lunar surface would occur.