The CFHT Large Area U-band Deep Survey (CLAUDS) uses data taken with the MegaCam mosaic imager on CFHT to produce images of 18.60 deg2 with median seeing of FWHM=0.92 arcsec and to a median depth of U = 27.1 AB (5 sigma in 2 arcsec apertures), with selected areas that total 1.36 deg2 reaching a median depth of U=27.7 AB. These are the deepest U-band images assembled to date over this large an area. These data are located in four fields also imaged to comparably faint levels in grizy and several narrowband filters as part of the Hyper Suprime-Cam (HSC) Subaru Strategic Program (HSC-SSP). These CFHT and Subaru datasets will remain unmatched in their combination of area and depth until the advent of the Large Synoptic Survey Telescope (LSST). This paper provides an overview of the scientific motivation for CLAUDS and gives details of the observing strategy, observations, data reduction, and data merging with the HSC-SSP. Three early applications of these deep data are used to illustrate the potential of the dataset: deep U-band galaxy number counts, z~3 Lyman break galaxy (LBG) selection, and photometric redshifts improved by adding CLAUDS U to the Subaru HSC grizy photometry.