We have obtained images of 11 fields in the Trapezium cluster with the Planetary Camera (PC) of the Hubble Space Telescope (HST) in order to extend Herbig & Terndrup's (1986) study of this prototype, dense embedded cluster to fainter magnitudes than is possible from the ground. Using these images, we have identified 319 stars within an area of approximately 12 sq arc min corresponding roughly to a volume of approximately 0.065 cu pc assuming the cluster is approximately spherically symmetric. Our completeness limits for star identification in V-band and I-band images are V approximately = 20 and I(sub c) approximately = 19 respectively, corresponding to a mass limit of approximately 0.15 solar mass if the faintest stars have the same average A(sub v) as that estimated for the brighter stars in the cluster. We have compared the V versus V-I color-magnitude diagram derived from the HST photometry to new theoretical isochrones. Star formation in the Trapezium appears to be remarkably coeval, with greater than or = 80% of the stars having inferred ages less than 1 Myr. Over the somewhat limited mass range of the observations, there is no evidence for 'bimodal' star formation-the high- and low-mass stars appear to have the same ages. The sharp cores of the HST images and the small angular size of the PC pixels has allowed us to identify 35 new visual binaries in the cluster with separations from approximately 0.06 arc sec (approximately 26 AU) to approximately 1.0 arc sec (approximately 440 AU). For the range of binary separations that we are sensitive to, the observed binary frequency for the Trapezium is essentially identical to that estimated for field low-mass stars by Duquennoy & Mayor (1991). The most straightfoward inference from this result is that binaries in this separation are unlikely to be formed by a tidal capture process. We have also identified three stars which have associated compact nebulosity visible in the HST images. One of these star + nebulosity cases was previously identified by O'Dell, Wen, & Hu (1993)-these objects appear to form a class of objects whose circumstellar matter is being 'lit up', most likely by Theta(sup 1) Ori C, enabling the gas to be observable at both optical and radio wavelengths (Felli et al. 1993a, b). We provide a brief summary of the optical properties of the other radio sources which appear in our PC images.