The CCAT-prime (CCAT-p) project aims to construct a 6-meter diameter telescope with a surface accuracy of 7-10 μm at 5600 meter elevation on Cerro Chajnantor in Chile. Implementation of a novel crossed-Dragone optical design will deliver a high-throughput wide-field-of-view telescope capable of illuminating >105 millimeter wavelength detectors. The 5600 meter site enables routine access to the 350 μm window as well as improved performance at longer wavelengths and, under best conditions, access to the 200 μm window. CCAT-p is specifically designed to measure the kinematic Sunyaev-Zel’dovich effect of galaxy clusters, to trace the appearance of the first population of star-forming galaxies through intensity mapping of their [CII] emission in the epoch of reionization, and to probe multiple spectral line tracers of the ISM over a range of environments in the Milky Way, Magellanic Clouds and other nearby galaxies. It will also be a next-generation Cosmic Microwave Background observatory.The CCAT consortium includes Cornell University; the University of Colorado at Boulder, the University of Cologne and the University of Bonn; McGill University, McMaster University, the University of British Columbia, the University of Calgary, the University of Toronto, the University of Waterloo, Dalhousie University, the Western University; and Associated Universities, Inc. CCAT operates in Chile thanks to a Cooperative Agreement with the University of Chile and under the auspices of the Ministry of Foreign Affairs of Chile.