We present new Atacama Large Millimeter Array (ALMA) observations towards NGC 4725 B, a discrete, compact, optically-faint region within the star-forming disk of the nearby galaxy NGC 4725 that exhibits strong anomalous microwave emission (AME). These new ALMA data include continuum observations centered at 92, 133, 203, and 221 GHz accompanied by spectral observations of the $^{12}$CO ($J=2rightarrow1$) line. NGC 4725 B is detected in the continuum at all frequencies, although the detection at 203 GHz is marginal. While molecular gas is not detected at the exact location of NGC 4725 B, there is molecular gas in the immediate vicinity (i.e., $lesssim 100$ pc) along with associated diffuse 8 $mu$m emission. When combined with existing Very Large Array continuum data at 1.5, 3, 5.5, 9, 14, 22, 33, and 44 GHz, the spectrum is best fit by a combination of AME, synchrotron, and free-free emission that is free-free absorbed below $sim6$ GHz. Given the strength of the AME, there is surprisingly no indication of millimeter dust emission associated with NGC 4725 B on $lesssim$6arcsec~spatial scales at the sensitivity of the ALMA interferometric data. Based on the properties of the nearest molecular gas complex and the inferred star formation rate, NGC 4725 B is consistent with being an extremely young ($sim 3-5$ Myr) massive ($lesssim 10^{5} M_{odot}$) cluster that is undergoing active cluster feedback. However, the lack of millimeter thermal dust emission is difficult to reconcile with a spinning dust origin of the 30 GHz emission. On the other hand, modeling NGC 4725 B as a new class of background radio galaxy is also unsatisfactory.
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