In the very heavy collision system Au-197 + Au-197 the K+ production process was studied as a function of impact parameter at 1 GeV/nucleon, a beam energy well below the free N-N threshold. The K+ multiplicity increases more than linearly with the number of participant nucleons and the K+/pi+ ratio rises significantly when going from peripheral to central collisions. The measured K+ double differential cross section is enhanced by a factor of 6 compared to microscopic transport calculations if secondary processes (DELTAN --> K LAMBDA N and DELTADELTA --> K LAMBDA N) are ignored.