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 \sim 10 ^ { 28 } erg s ^ { -1 } , we detect 127 X-ray sources , most with sub-arcsecond 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 YSO population spans a range of \log L _ { x } \simeq 28.0 to 31.5 erg s ^ { -1 } in the 0.5 - 8 keV band , and absorption ranges from \log N _ { H } \simeq 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 \sim 7 keV . Comparison with K-band source counts indicates that we detect all of the known cluster members with K < 12 , and about half of members with K > 12 . K \simeq 11 , the peak of the K-band luminosity function , corresponds to 0.2 - 0.4 M _ { \odot } stars for a cluster age of \sim 1 Myr . We detect seven of the twenty 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 which 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 L _ { x } \propto J is seen which confirms the well-known relation L _ { x } \propto L _ { bol } found in many star forming regions . Based on spectral analysis for the X-ray counterpart of SVS 16 , we establish that the column density N _ { H } is much lower than that expected from near-IR photometry so that its X-ray luminosity , \log L _ { x } \simeq 30.6 erg s ^ { -1 } , is not unusually high .