  A semiclassical theory is developed for the appearance of an excitation gap
in a ballistic chaotic cavity connected by a point contact to a superconductor.
Diffraction at the point contact is a singular perturbation in the limit
$\hbar\to 0$, which opens up a gap $E_{\rm gap}$ in the excitation spectrum.
The time scale $\hbar/E_{\rm gap}\propto\alpha^{-1}\ln\hbar$ (with $\alpha$ the
Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of
quantum chaos.
