The authors have obtained a deep (53 ks) X-ray image of the very young stellar cluster IC 348 with the Advanced CCD Imaging Spectrometer on board the Chandra X-Ray Observatory. In this image with a sensitivity limit of ~ 1 x 10²⁸ ergs/s (more than 10 times deeper than their ROSAT images of IC 348), 215 X-ray sources were detected. While 115 of these sources can be identified with known cluster members, 58 X-ray sources are most likely new, still unidentified cluster members. About 80% of all known cluster members with masses between ~0.15 and 2 solar masses are visible as X-ray sources in the ACIS image. X-ray emission at levels of ~10²⁸ ergs/s was discovered from four of 13 known brown dwarfs and from three of 12 brown dwarf candidates in IC 348. X-ray emission was also detected from two deeply embedded objects, presumably class I protostars, south of the cluster center. Optical and infrared counterparts have been identified for most of the X-ray sources. Some 40 X-ray sources do not have optical or IR counterparts, and are most likely background (probably extragalactic) objects. This number is consistent with the expected number of extragalactic background X-ray sources based on the observed log N - log S statistics from the deep X-ray counts in the Chandra Deep Field South. This table was created by the HEASARC in January 2007 based on the merger of CDS table J/AJ/122/866/table1.dat (Table 1 from Preibisch and Zinnecker 2001) with the electronic AJ table version of Table 1 from Preibisch and Zinnecker 2002. This is a service provided by NASA HEASARC .