We report on the discovery of an apparently normal galaxy at z = 1.018, designated G0333 + 3208, found during a long-slit search for faint emission-line objects. One strong emission line has been detected in the wavelength range 3800-8500 angstrom, which we attribute to [O II] lambda-3727. The object is a approximately 24 mag galaxy with a relatively flat optical spectrum. There are no morphological or spectroscopic signs of an active nucleus in the object, or in its vicinity, and no radio flux from the object down to 200 mu-Jy rms at lambda = 20 cm. From the emission-line flux, assuming photoionization by young stars and a normal IMF, we estimate a star formation rate of approximately 3.5h-2 M. yr-1 (for OMEGA-0 = 1). This object would thus be among the most distant of normal galaxies now known. It may be representative of the faint blue or flat-spectrum population, which dominates deep galaxy counts.