Certain reactor safety instrument channels require the assured detection of weak neutron bursts in the presence of strong gamma background. Inasmuch as the importance of some such channel justifies a fairly elaborate detection system, neutron multiplication suggests itself as a means of enhancing the signal strength relative to the background. While such a system may be technically feasible, it is subject to severe limitations inherent in the statistical nature of multiplication, which are explored in this Note. In particular, it is shown that, given a reasonably high intrinsic neutron detection efficiency, the statistical quality of detection is optimized for relatively weak multiplication factors and worsens again as multiplication increases. The overall design of a multiplying detection system is in fact a matter of considerable complexity since multiplication affects source geometry and energy distribution as well as statistics. A potential application is the detection of fuel failures in a liquid metal fast breeder reactor (LMFBR) plant by monitoring the coolant flow system for delayed neutrons downstream from the core.