We use 8.3 um mid-infrared images acquired with the Midcourse Space Experiment satellite to identify and catalog Infrared Dark Clouds (IRDCs) in the first and fourth quadrants of the Galactic plane. Because IRDCs are seen as dark extinction features against the diffuse Galactic infrared background, we identify them by first determining a model background from the 8.3 um images and then searching for regions of high decremental contrast with respect to this background. IRDC candidates in our catalog are defined by contiguous regions bounded by closed contours of a 2 sigma decremental contrast threshold. Although most of the identified IRDCs are actual cold, dark clouds, some as yet unknown fraction may be spurious identifications. For large, high contrast clouds, we estimate the reliability to be 82%. Low contrast clouds should have lower reliabilities. Verification of the reality of individual clouds will require additional data. We identify 10,931 candidate infrared dark clouds. For each IRDC, we also catalog cores. These cores, defined as localized regions with at least 40% higher extinction than the cloud's average extinction, are found by iteratively fitting 2-dimensional elliptical Gaussians to the contrast peaks. We identify 12,774 cores. The catalog contains the position, angular size, orientation, area, peak contrast, peak contrast signal-to-noise, and integrated contrast of the candidate IRDCs and their cores. The distribution of IRDCs closely follows the Galactic diffuse mid-infrared background and peaks toward prominent star forming regions, spiral arm tangents, and the so-called 5 kpc Galactic molecular ring.

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