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

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... s 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