  Using the joint distribution for proper time-delays of a chaotic cavity
derived by Brouwer, Frahm & Beenakker [Phys. Rev. Lett. {\bf 78}, 4737 (1997)],
we obtain, in the limit of large number of channels $N$, the large deviation
function for the distribution of the Wigner time-delay (the sum of proper
times) by a Coulomb gas method. We show that the existence of a power law tail
originates from narrow resonance contributions, related to a (second order)
freezing transition in the Coulomb gas.
