We present deep images of the field of gamma-ray burst (GRB) 990123 obtained in a broad-band UV/visible bandpass with the Hubble Space Telescope, and deep near-infrared images obtained with the Keck-I 10-m telescope. Both the HST and Keck images show that the optical transient (OT) is clearly offset by 0.6 arcsec from an extended object, presumably the host galaxy. This galaxy is the most likely source of the metallic-line absorption at z = 1.6004 seen in the spectrum of the OT. With magnitudes V_{C} ~ 24.6 +/- 0.2 and K = 21.65 +/- 0.30 mag this corresponds to an L ~ 0.7 L_* galaxy, assuming that it is located at z = 1.6. The estimated unobscured star formation rate is SFR ~ 6 M_sun/yr, which is not unusually high for normal galaxies at comparable redshifts. The strength of the observed metallic absorption lines is suggestive of a relatively high metallicity of the gas, and thus of a chemically evolved system which may be associated with a massive galaxy. It is also indicative of a high column density of the gas, typical of damped Ly$\alpha$ systems at high redshifts. We conclude that this is the host galaxy of GRB 990123. No other obvious galaxies are detected within the same projected radius from the OT. There is thus no evidence for strong gravitational lensing magnification of this burst, and some alternative explanation for its remarkable energetics may be required. The observed offset of the OT from the center of its apparent host galaxy, 5.5 +/- 0.9 proper kpc (projected) in the galaxy's rest-frame, both refutes the possibility that GRBs are related to galactic nuclear activity and supports models of GRBs which involve the death and/or merger of massive stars. Further, the HST image suggests an intimate connection of GRB 990123 and a star-forming region.