  We find a gravitational instanton that connects an initial state
corresponding to a single-centered extremal Reissner-Nordstrom (ERN) black hole
configuration, to a final state corresponding to a multi-centered
configuration. This instanton is interpreted as describing quantum tunneling
between the two different black hole solutions. We evaluate the Euclidean
action for this instanton and find that the amplitude for the tunneling process
is equal to half the difference in entropy between the initial and final
configurations.
