We discuss the nature of a discrete, compact radio source (NGC 4725 B) located $approx$1.9 kpc from the nucleus in the nearby star-forming galaxy NGC 4725, which we believe to be a new detection of extragalactic Anomalous Microwave Emission (AME). Based on detections at 3, 15, 22, 33, and 44 GHz, NGC 4725 B is a $mu$Jy radio source peaking at $approx$33 GHz. While the source is not identified in $BVRI$ photometry, we detect counterparts in the mid-infrared $Spitzer$/IRAC bands (3.6, 4.5, 5.8, 8.0 $mu$m) that appear to be associated with dust emission in the central region of NGC 4725. Consequently, we conclude that NGC 4725 B is a new detection of AME, and very similar to a recent detection of AME in an outer-disk star-forming region in NGC 6946. We find that models of electric dipole emission from rapidly rotating ultra-small grains are able to reproduce the radio spectrum for reasonable interstellar medium conditions. Given the lack of an optical counterpart and the shape of the radio spectrum, NGC 4725 B appears consistent with a nascent star-forming region in which young ($lesssim 3$ Myr) massive stars are still highly enshrouded by their natal cocoons of gas and dust with insufficient supernovae occurring to produce a measurable amount of synchrotron emission.
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