The Lyman resonance-absorption bands of interstellar molecular hydrogen have been observed in the far-ultraviolet spectrum of the star Persei. The column density of H2 is estimated to be about 1.3 X 1O cm . The colurnn density of interstellar atomic hydrogen, determined from the La absorption line in the same spectrum, is about 4.2 >c 1 cm . Hence, in this line of sight, where visual total extinction by dust is about 1 mag, nearly half of the total hydrogen may be in molecular form. This is in agreement with theoretical predictions.