  The Lyman-alpha emitters found at z=4.5 and 5.7 by the Large Area Lyman Alpha
(LALA) survey have high equivalent widths in the Lyman-alpha line. Such lines
can be produced by narrow-lined active galactic nuclei (AGNs) or by stellar
populations with a very high proportion of young, massive stars. To check for
Type-II (i.e., narrow-lined) quasars, we obtained a deep X-ray image of 49
Lyman-alpha sources in a single field of the ACIS instrument on the Chandra
X-ray Observatory. None of these sources were detected with a 3-sigma limiting
X-ray luminosity of 2.9x10^{43} ergs/s. For comparison, the two known high
redshift type-II quasars have luminosities of 4x10^{43} ergs/s before
extinction correction. The sources remain undetected in stacked images of the
49 lyman-alpha sources (with 6.5 Mega-seconds effective Chandra on-axis
exposure) at 3-sigma limits of 4.9x10^{42} ergs/s. The resulting X-ray to
lyman-alpha ratio is about 4-24 times lower than the ratio for known type-II
quasars, while the average Lyman-alpha luminosity of the LALA sample is in
between the two type-II's. The cumulative X-ray to Lyman-alpha ratio limit is
also below that of 90% of low-redshift Seyfert galaxies.
