  In an earlier work we had considered a Gaussian ensemble of random matrices
in the presence of a given external matrix source. The measure is no longer
unitary invariant and the usual techniques based on orthogonal polynomials, or
on the Coulomb gas representation, are not available. Nevertheless the n-point
correlation functions are still given in terms of the determinant of a kernel,
known through an explicit integral representation. This kernel is no longer
symmetric though and is not readily accessible to standard methods. In
particular finding the level spacing probability is always a delicate problem
in Fredholm theory, and we have to reconsider the problem within our model. We
find a new class of universality for the level spacing distribution when the
spectrum of the source is ajusted to produce a vanishing gap in the density of
the state. The problem is solved through coupled non-linear differential
equations, which turn out to form a Hamiltonian system. As a result we find
that the level spacing probability $p(s)$ behaves like $\exp[ - C
s^{{8\over{3}}}]$ for large spacing $s$; this is consistent with the asymptotic
behavior $\exp[ - C s^{2 \beta + 2}]$, whenever the density of state behaves
near the edge as $\rho(\lambda)\sim \lambda^{\beta}$.
