An optical spectrum of the afterglow from the unusually bright gamma-ray burst GRB 990123 obtained on 24.25 January 1999 universal time showed an absorption system at a redshift of z = 1.600. The absence of a hydrogen Lyman alpha forest sets an upper limit of z < 2.17, whereas ultraviolet photometry indicates an upper limit of z < 2.05. The probability of intersecting an absorption system as strong as the one observed along a random line of sight out to this z is at most a few percent, implying that GRB 990123 was probably at z = 1. 600. Currently favored cosmological parameters imply that an isotropic energy release equivalent to the rest mass of 1.8 neutron stars (4.5 x 10(54) erg) was emitted in gamma rays. Nonisotropic emission, such as intrinsic beaming, may resolve this energy problem.