Using a quantum kinetic equation we study the possibility that focused beam
s at proposed x-ray free electron laser facilities can initiate spontaneous
electron-positron pair production from the QED vacuum. Under conditions re
ckoned achievable at planned facilities, repeated cycles of particle creati
on and annihilation will take place in tune with the laser frequency. The p
eak particle number density is insensitive to this frequency, and one can a
nticipate the production of a few hundred particle pairs per laser period.