  We study the transition between integrable and chaotic behaviour in
dissipative open quantum systems, exemplified by a boundary driven quantum
spin-chain. The repulsion between the complex eigenvalues of the corresponding
Liouville operator in radial distance $s$ is used as a universal measure. The
corresponding level spacing distribution is well fitted by that of a static
two-dimensional Coulomb gas with harmonic potential at inverse temperature
$\beta\in[0,2]$. Here, $\beta=0$ yields the two-dimensional Poisson
distribution, matching the integrable limit of the system, and $\beta=2$ equals
the distribution obtained from the complex Ginibre ensemble, describing the
fully chaotic limit. Our findings generalise the results of Grobe, Haake and
Sommers who derived a universal cubic level repulsion for small spacings $s$.
We collect mathematical evidence for the universality of the full level spacing
distribution in the fully chaotic limit at $\beta=2$. It holds for all three
Ginibre ensembles of random matrices with independent real, complex or
quaternion matrix elements.
