We report on the measurement of the specific activity of 39Ar in natural argon. The measurement was performed with a 2.3-l two-phase (liquid and gas) argon drift chamber. The detector was developed by the WARP Collaboration as a prototype detector for WIMP Dark Matter searches with argon as a target. The detector was operated for more than two years at Laboratori Nazionali del Gran Sasso, Italy, at a depth of 3400 m w.e. The specific activity measured for 39Ar is 1.01±0.02(stat)±0.08(syst)Bq per kg of natAr.