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 2.9 \times 10 ^ { 43 } ergs/s . For comparison , the two known high redshift type-II quasars have luminosities of 4 \times 10 ^ { 43 } ergs/s before extinction correction . The sources remain undetected in stacked images of the 49 Lyman- \alpha sources ( with 6.5 Ms effective Chandra on-axis exposure ) at 3 \sigma limits of 4.9 \times 10 ^ { 42 } . 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 .