In this first of two companion papers on the Orion Nebula Cluster (ONC), we present our analysis of a 63 ks Chandra HRC-I observation that yielded 742 X-ray detections within the 30' × 30' field of view. To facilitate our interpretation of the X-ray image, here we collect a multiwavelength catalog of nearly 2900 known objects in the region by combining 17 different catalogs from the recent literature. We define two reference groups: an infrared sample, containing all objects detected in the K band, and an optical sample comprising low-extinction, well-characterized ONC members. We show for both samples that field object contamination is generally low. Our X-ray sources are primarily low-mass ONC members. The detection rate for optical sample stars increases monotonically with stellar mass from zero at the brown dwarf limit to ~100% for the most massive stars but shows a pronounced dip between 2 and 10 M. We determine L_X and L_X/L_bol for all stars in our optical sample and utilize this information in our companion paper to study correlations between X-ray activity and other stellar parameters.