We present the first measurement of fluctuations from event to event in the
production of strange particles in collisions of heavy nuclei. The ratio o
f charged kaons to charged pions is determined for individual central Pb Pb collisions. After accounting for the fluctuations due to detector resolu
tion and finite number statistics we derive ant upper limit on genuine nons
tatistical fluctuations, which could be related to a first- or second-order
QCD phase transition. Such fluctuations Lire shown to be very small.