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)
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