  We present near-infrared long-slit spectra of eight optically-dim X-ray
sources obtained with ISAAC on the Very Large Telescope. Six of the sources
have hard X-ray emission with a significant fraction of the counts emerging
above 2 keV. All were discovered serendipitously in the fields of three nearby
galaxy clusters observed with Chandra, and identified through near-infrared
imaging. The X-ray fluxes lie close to the break in the source counts. Two of
the sources show narrow emission lines, and a third has a broad line. One of
the narrow line-emitting sources has a clear redshift identification at z=2.18,
while the other has a tentative determination based on the highest redshift
detection of He I 10830 at z=1.26. The remainder have featureless spectra to
deep limiting equivalent widths of 20--60 angstroms and line flux approx= 5 x
10^{-17} erg/s/cm^2 in the K-band. High-quality J, H and Ks--band images of the
sources were combined with archival optical detections or limits to estimate a
photometric redshift for six. Two sources show complex double morphology. The
hard sources have spectral count ratios consistent with heavily obscured AGN,
while the host galaxy emits much of the optical and near-infrared flux. The
most likely explanation for the featureless continua is that the line photons
are being scattered or destroyed by optically-thick gas and associated dust
with large covering fractions.
