  We present an analysis of a deep, 172 ks Chandra observation of the Large
Area Lyman Alpha Survey (LALA) Bo\"{o}tes field, obtained with the Advanced CCD
Imaging Spectrometer (ACIS-I) on the Chandra X-ray Observatory. This is one of
the deepest Chandra images of the extragalactic sky; only the 2 Ms CDF-N and 1
Ms CDF-S are substantially deeper. A total of 168 X-ray sources were detected.
The X-ray source counts were derived and compared with those from other Chandra
deep surveys; the hard X-ray source density of the LALA Bo\"{o}tes field is 33%
higher than that of CDF-S at the flux level of 2.0E-15 ergs/cm^2/s, confirming
the field-to-field variances of the hard band source counts reported by
previous studies. The deep exposure resolves > 72% of the 2-10 keV X-ray
background.
  Our primary optical data are R-band imaging from NOAO Deep Wide-Field Survey
(NDWFS), with limiting magnitude of R = 25.7 (Vega, 3sigma, 4" diameter
aperture). We have found optical counterparts for 152 of the 168 Chandra
sources (90%). Among the R-band non-detected sources, not more than 11 of them
can possibly be at z > 5, based on the hardness ratios of their X-ray emission
and nondetections in bluer bands. The majority (~76%) of the X-ray sources are
found to have log(f_X/f_R) within 0.0+-1, which are believed to be AGNs.Most of
the X-ray faint/optically bright sources (log(f_X/f_R) < -1.0) are optically
extended, which are low-z normal galaxies or low luminosity AGNs. There is also
a population of sources which are X-ray overluminous for their optical
magnitudes (log(f_X/f_R) > 1.0), which are harder in X-ray and are probably
obscured AGNs. (abridged)
