The magnetic field within the core of a coronal mass ejection (CME) on 2010 August 14 is derived from analysis of multi-wavelength radio imaging data. This CME's core was found to be the source of a moving type IV radio burst, whose emission is here determined to arise from the gyrosynchrotron process. The CME core's true trajectory, electron density, and line-of-sight depth are derived from stereoscopic observations, constraining these parameters in the radio emission models. We find that the CME carries a substantial amount of mildly relativistic electrons (E < 100 keV) in a strong magnetic field (B < 15 G), and that the spectra at lower heights are preferentially suppressed at lower frequencies through absorption from thermal electrons. We discuss the results in light of previous moving type IV burst studies, and outline a plan for the eventual use of radio methods for CME magnetic field diagnostics.