We report the probable identification of the X-ray counterpart to the γ-ray pulsar PSR J2021+ 4026 using imaging with the Chandra X-ray Observatory Advanced CCD Imaging Spectrometer and timing analysis with the Fermi satellite. Given the statistical and systematic errors, the positions determined by both satellites are coincident. The X-ray source position is RA 20 h 21 m 30 fs 733, decl.+ 40 26'46 farcs 04 (J2000) with an estimated uncertainty of 1 farcs 3 combined statistical and systematic error. Moreover, both the X-ray to γ-ray and the X-ray to optical flux ratios are sensible assuming a neutron star origin for the X-ray flux. The X-ray source has no cataloged infrared-to-visible counterpart and, through new observations, we set upper limits to its optical emission of i'> 23.0 mag and r'> 25.2 mag. The source exhibits an X-ray spectrum with most likely both a power law and a thermal component. We also report on the X-ray and visible light properties of the 43 other sources detected in our Chandra observation.