We present early- and late-time photometric and spectroscopic observations of supernova (SN) 2009hd in the nearby spiral galaxy NGC 3627 (M66). This SN is one of the closest to us in recent years and provides an uncommon opportunity to observe and study the nature of SNe. However, the object was heavily obscured by dust, rendering it unusually faint in the optical given its proximity. We find that the observed properties of SN 2009hd support its classification as a possible Type II-Linear SN (SN II-L), a relatively rare subclass of core-collapse SNe. High-precision relative astrometry has been employed to attempt to identify an SN progenitor candidate, based on a pixel-by-pixel comparison between Hubble Space Telescope (HST) F555W and F814W images of the SN site prior to explosion and at late times. A progenitor candidate is identified in the F814W images only; this object is undetected in F555W. Significant uncertainty exists in the astrometry, such that we cannot definitively identify this object as the SN progenitor. Via insertion of artificial stars into the pre-SN HST images, we are able to constrain the progenitor's properties to those of a possible supergiant, with intrinsic absolute magnitude M 0 F555W >~ -7.6 mag and intrinsic color (V - I)0 >~ 0.99 mag. The magnitude and color limits are consistent with a luminous red supergiant (RSG); however, they also allow for the possibility that the star could have been more yellow than red. From a comparison with theoretical massive-star evolutionary tracks which include rotation and pulsationally enhanced mass loss, we can place a conservative upper limit on the initial mass for the progenitor of M ini <~ 20 M &sun;. If the actual mass of the progenitor is near the upper range allowed by our derived mass limit, then it would be consistent with that for the identified progenitors of the SN II-L 2009kr and the high-luminosity SN II-Plateau (II-P) 2008cn. The progenitors of these three SNe may possibly bridge the gap between lower-mass RSGs that explode as SNe II-P and luminous blue variables, or more extreme RSGs, from which the more exotic SNe II-narrow may arise. Very late time imaging of the SN 2009hd site may provide us with more clues regarding the true nature of its progenitor.