We report the detection of a faint narrow HI absorption line at a redshift of 3.38 against the quasar PKS 0201+113 which itself has an emission redshift of 3.61. The absorption line redshift agrees, to within the errors, with that of a damped Ly alpha line. The line has a halfwidth of about 9 km s(-1). Comparing the line equivalent width with the HI column density of the neutral gas we deduce a spin temperature for the gas of about 1100 K. In view of the fact that the spin temperature is remarkably similar to that derived for other high redshift absorption systems we consider it unlikely that it is due to different lines-of-sight for the ultraviolet continuum and the compact radio source. The high spin temperature may reflect a high kinetic...