We report on the first experimental determination of the hyperfine structure of the 1s(5)-2p(9) transition in (39)Ar. We give a detailed description of the sample preparation, spectroscopy cell cleaning, and spectroscopic setup. The resulting set of parameters consists of the hyperfine constants of the levels involved and the isotopic shift between (39)Ar and (40)Ar. With the achieved precision all laser frequencies necessary for the implementation of atom trap trace analysis for (39)Ar, i.e., laser cooling and repumping frequencies, are now known.