  We report observations of spontaneous formation of magnetic flux lines during
a rapid quench of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films through T$_{c}$. This
effect is predicted according to the Kibble-Zurek mechanism of creation of
topological defects of the order parameter during a symmetry-breaking phase
transition. Our previous experiment, at a quench rate of 20K/sec, gave null
results. In the present experiment, the quench rate was increased to
\TEXTsymbol{>} 10$^{8}$ K/sec. Within experimental resolution, the dependence
of the measured flux on the cooling rate is consistent with the prediction.
