Spectrophotometric and broad-band infrared observations are reported for the most luminous quasar S5 0014+81. H-beta and the forbidden line of O III in the 4959+5007 A emission lines are detected at a redshift of 3.41, in agreement with the optically determined redshift. S5 0014+81 is the first object at such high redshift in which H-beta and the forbidden line of O III have been measured separately, showing rest frame equivalent widths of 37 and 31 A, respectively. The relatively high Ly-alpha/H-beta ratio of 10.5 may be shaped by radiative transfer processes with little or no internal reddening. At the high-luminosity end represented by this quasar, a narrow-line region seems to be well established; the O III forbidden lines still seem to act as luminosity indicators over six and one-half orders of magnitude.