Designing low-cost filterbanks is important due to severe resource limitations imposed by hearing aid size. Here, we develop a novel FIR filterbank employing stochastic computing (SC). SC-based filters use (pseudo)-random bit-streams to efficiently perform the core filtering operation. We demonstrate that SC is well-suited to low-cost filterbank design and compare our SC filterbank to a conventional sequential binary (SB) design. We show that the SC design achieves the same accuracy and latency as the SB one, with an exceptionally large 70% reduction in chip area. The power consumption of our proposed SC filterbank is 38-96% that of the SB design.