Advanced molecular nanotechnology devices are expected to have exceedingly high transient fault rates and large numbers of inherent device defects compared to conventional CMOS devices. We introduce the Recursive NanoBox Processor Grid as an application specific, fault-tolerant, parallel computing system designed for fabrication with unreliable nanotechnology devices. In this initial study we construct VHDL models of the NanoBox Processor cell ALU and evaluate the effectiveness of our recursive fault masking approach in the presence of random transient errors. Our analysis shows that the ALU can calculate correctly 100 percent of the time with raw FIT (failures in time) rates as high as 10{23}. We achieve this error correction with an area overhead on the order of 9x, which is quite reasonable given the high integration densities expected with nanodevices.