  The emergence of chaotic phenomena in a quantum system has long been an
elusive subject. Experimental progresses in this subject have become urgently
needed in recent years, when considerable theoretical studies have unveiled the
vital roles of chaos in a broad range of topics in quantum physics. Here, we
report the first experimental observation of time singularity, that signals a
classical-to-quantum chaos transition and finds its origin in the {\it sudden
change} in system's memory behaviors. The time singularity observed is an
analog of the "dynamical quantum phase transition" (DQPT) -- proposed very
recently for regular systems -- in chaotic systems, but with totally different
physical origin.
