NGC 1333, a highly active star formation region within the Perseus molecular cloud complex, has been observed with the ACIS-I detector on board the Chandra X-Ray Observatory. In our image with a sensitivity limit of ~1028 ergs s-1, we detect 127 X-ray sources, most with subarcsecond positional accuracy. While 32 of these sources appear to be foreground stars and extragalactic background, 95 X-ray sources are identified with known cluster members. The X-ray luminosity function of the discovered young stellar object (YSO) population spans a range of log LX 28.0-31.5 ergs s-1 in the 0.5-8 keV band, and absorption ranges from log NH 20 to 23 cm-2. Most of the sources have plasma energies between 0.6 and 3 keV, but a few sources show higher energies up to ~7 keV. Comparison with K-band source counts indicates that we detect all of the known cluster members with K 12. K 11, the peak of the K-band luminosity function, corresponds to 0.2-0.4 M☉ stars for a cluster age of ~1 Myr. We detect seven of the 20 known YSOs in NGC 1333 producing jets or molecular outflows as well as one deeply embedded object without outflows. No evident difference in X-ray emission of young stars with and without outflows is found. Based on the complete subsample of T Tauri stars, we also find no difference in X-ray properties and X-ray production mechanism of stars with and without K-band excess disks. Several other results are obtained. We suggest that the X-ray emission from two late B stars that illuminate the reflection nebula originates from unresolved late-type companions. Two T Tauri stars are discovered in the ACIS images as previously unknown components of visual binaries. A good correlation LX J is seen, which confirms the well-known relation LX Lbol found in many star-forming regions. Based on spectral analysis for the X-ray counterpart of SVS 16, we establish that the column density NH is much lower than that expected from near-IR photometry so that its X-ray luminosity, log LX 30.6 ergs s-1, is not unusually high.

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