We present the results of a very deep ROSAT HRI X-ray observation of t
he highly active star forming region NGC 1333. In total we could detec
t 20 X-ray sources, 16 of which we assume to be members to the cluster
of pre main sequence stars. Since most of the stars in NGC 1333 are s
till deeply embedded in the molecular cloud (A(V) less than or similar
to 5-30 mag), we use near infrared data to estimate individual extinc
tions for the calculation of X-ray luminosities.One of the X-ray sourc
es is identified with the optically invisible, very deeply embedded(A(
V) approximate to 28 mag) infrared class I source SVS16, for which we
find an extremely high X-ray luminosity of 2.8 x 10(32) erg/sec, makin
g this object one of the most X-ray luminous pre main sequence stars k
nown to date. Since we have already performed similar sensitive ROSAT
observations of the young cluster IC 348 (the second active star formi
ng region in the Perseus molecular cloud complex), we compare the X-ra
y properties of the young stars in NGC 1333 to those in IC 348. We fin
d no evidence for a significant change of the X-ray luminosity functio
n during the first few million years in the life of the pre main seque
nce stars.