The Fourth Uhuru (4U) Catalog lists 339 X-ray sources that were observed with the Uhuru (SAS A) X-ray observatory. It contains positional information in the form of 90% confidence level error boxes, 2-6keV intensities, possible optical and radio counterparts, and alternative names for sources observed in earlier compilations. The major classes of identified objects include binary stellar systems, supernova remnants, Seyfert galaxies, clusters of galaxies, and possibly the new class of superclusters of galaxies. The Uhuru satellite was a scanning X-ray instrument with a narrow (1 by 10 degree FWFM) and a wide (10 by 10 degree FWFM) collimator (cf. Giacconi et al. 1971ApJ...165L..27G). Typically, the scan rate was 0.5degree/second, with the spin axis in one position for roughly one day. During the interval for which the spin axis was fixed, repeated scans were made of the same 10 by 360 degrees band of the sky. For this catalog, the individual scans were superposed using aspect data from an orthogonally mounted triad of magnetometers and a Sun sensor onboard the spacecraft, supplemented by observations of well-located X-ray sources. The observations employed in producing this catalog were obtained over a total of 429 days between 1970 December 12 and 1973 March 18, apart from a gap between 1972 July and December when the spacecraft's transmitter was operating improperly.