The linac booster (LIBO) project aims to build a 3 GHz proton linac to give the beam from 50-70 MeV cyclotrons, which exist in several laboratories and hospitals, a final energy of 200 MeV. This will allow the treatment of deep-seated tumours. A prototype of the first LIBO module was designed, constructed and RF tested by a collaboration of CERN, University and INFN of Milan, University and INFN of Naples, and the TERA Foundation. Low power RF measurements have shown good field uniformity and stability along the axis of the four tanks composing the LIBO module. In December 2000, full power RF measurements at a repetition rate of 100 Hz have been performed at CERN. After a very short conditioning period, an accelerating gradient approaching 30 MV/m has been easily achieved in the tanks, well above the nominal 15.8 MV/m. The particularities of the design and the reasons for the successful performance are discussed.