We present a new, objectively defined catalog of candidate galaxy clusters based on the galaxy catalogs from the Digitized Second Palomar Observatory Sky Survey (DPOSS). This cluster catalog, derived from the best calibrated plates in the high latitude (|b|>30) Northern Galactic Cap region, covers 5,800 square degrees, and contains 8,155 candidate clusters. A simple adaptive kernel density mapping technique, combined with the SExtractor object detection algorithm, is used to detect galaxy overdensities, which we identify as clusters. Simulations of the background galaxy distribution and clusters of varying richnesses and redshifts allow us to optimize detection parameters, and measure the completeness and contamination rates for our catalog. Cluster richnesses and photometric redshifts are measured, using integrated colors and magnitudes for each cluster. An extensive spectroscopic survey is used to confirm the photometric results. This catalog, with well-characterized sample properties, provides a sound basis for future studies of cluster physics and large scale structure. Comment: 49 pages, 16 figures. Accepted to AJ; appearing in April. Version with full resolution figures, and full length tables available at http://dposs.caltech.edu:8080/NoSOCS.html