We present the analysis of archival data from the Advanced Satellite for Cosmology and Astrophysics of the supernova remnant (SNR) G39.2-0.3. G39.2-0.3 has been sometimes characterized as a shell-like remnant in the literature, but our high-energy imaging and spectral analysis show the unambiguous composite nature of the remnant. We find that part of the contribution to the X-ray emission of G39.2-0.3 is distinctly nonthermal, best described by a power law with a photon index (2.53+0.34–0.27). The region of emission is consistent with a point source (extension consistent with the point-spread function of the detector at the off-axis angle of the observation) and is roughly defined by a circle of radius ∼4'. A second contribution comes from a thermal component, which contributes flux primarily at low energies. Despite the absence of any pulsed emission detected from the compact source, we argue that the emission is most probably due to a rotating compact object that is powering the detected synchrotron nebula within the SNR.