  We calculate the sample-to-sample fluctuations in the excitation gap of a
chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum
fluctuations on the order of magnitude of the level spacing, predicted by
random-matrix theory, apply if $\tau_E\ll\hbar/E_T$ (with $\tau_E$ the
Ehrenfest time and $E_T$ the Thouless energy). For $\tau_E\agt\hbar/ E_T$ the
fluctuations are much greater than the level spacing. We demonstrate the
quasiclassical nature of the gap fluctuations in the large-$\tau_E$ regime by
correlating them to an integral over the classical dwell-time distribution.
