We present our first results on field X-ray sources detected in a deep , 184.7 ks observation with the Advanced CCD Imaging Spectrometer ( ACIS-I ) on the Chandra X-Ray Observatory . The observations target the Lynx field ( \alpha _ { J 2000 } = 08 ^ { h } 48 ^ { m } , \delta _ { J 2000 } = +44 ^ { \circ } 54 \arcmin ) of SPICES , the Spectroscopic Photometric Infrared-Chosen Extragalactic Survey , which contains three known X-ray-emitting clusters at redshifts of z = 0.57 , 1.26 , and 1.27 . Not including the known clusters , in the 17 \arcmin \times 17 \arcmin ACIS-I field we detect 132 sources in the 0.5 - 2 keV ( soft ) X-ray band down to a limiting flux of \approx 1.7 \times 10 ^ { -16 } { ergs cm ^ { -2 } s ^ { -1 } } and 111 sources in the 2 - 10 keV ( hard ) X-ray band down to a limiting flux of \approx 1.3 \times 10 ^ { -15 } { ergs cm ^ { -2 } s ^ { -1 } } . The combined catalog contains a total of 153 sources , of which 42 are detected only in the soft band and 21 are detected only in the hard band . Confirming previous Chandra results , we find that the fainter sources have harder X-ray spectra , providing a consistent solution to the long-standing ‘ spectral paradox ’ . From deep optical and near-infrared follow-up data , 77 % of the X-ray sources have optical counterparts to I = 24 and 71 % of the X-ray sources have near-infrared counterparts to K _ { s } = 20 . Four of the 24 sources in the near-IR field are associated with extremely red objects ( EROs ; I - K _ { s } \geq 4 ) . We have obtained spectroscopic redshifts with the Keck telescopes of 18 of the Lynx Chandra sources . These sources comprise a mix of broad-lined active galaxies/quasars , apparently normal galaxies , and two late-type Galactic dwarfs . Intriguingly , one Galactic source is identified with an M7 dwarf exhibiting non-transient , hard X-ray emission . Thirteen of the Chandra sources are located within regions for which we have Hubble Space Telescope imaging . Nine of the sources are detected , showing a range of morphologies : several show compact cores embedded within diffuse emission , while others are spatially extended showing typical galaxy morphologies . Two of the Chandra sources in this subsample appear to be associated with mergers . We briefly review non-AGN mechanisms to produce X-ray emission and discuss properties of the Lynx Chandra sample in relation to other samples of X-ray and non-X-ray sources .