We report the discovery of a third ULX in NGC 925 (ULX-3), detected in November 2017 by Chandra at a luminosity of $L_{rm X} = (7.8pm0.8)times10^{39}$ erg s$^{-1}$. Examination of archival data for NGC 925 reveals that ULX-3 was detected by Swift at a similarly high luminosity in 2011, as well as by XMM-Newton in January 2017 at a much lower luminosity of $L_{rm X} = (3.8pm0.5)times10^{38}$ erg s$^{-1}$. With an additional Chandra non-detection in 2005, this object demonstrates a high dynamic range of flux of factor >26. In its high-luminosity detections, ULX-3 exhibits a hard power-law spectrum with $Gamma=1.6pm0.1$, whereas the XMM-Newton detection is slightly softer, with $Gamma=1.8^{+0.2}_{-0.1}$ and also well-fitted with a broadened disc model. The long-term light curve is sparsely covered and could be consistent either with the propeller effect or with a large-amplitude superorbital period, both of which are seen in ULXs, in particular those with neutron star accretors. Further systematic monitoring of ULX-3 will allow us to determine the mechanism by which ULX-3 undergoes its extreme variability and to better understand the accretion processes of ULXs.