The results of 23 km/s resolution echelle spectroscopy of the Lyman forest region of the z = 3.38 QSO 0014+813 are described. Voigt profile fits to the Lyman series absorption lines yield H I column density and Doppler parameter distributions similar to those obtained in three previous studies of other objects. There is no evidence so far of significant changes of the behavior of these distributions with redshift, except for the number of systems per unit redshift which, for log N(H I) > 13.75 (cgs), is proportional to (1+z) 2.1