  In this paper, we are concerned with a Kirchhoff problem in the presence of a
strongly-singular term perturbed by a discontinuous nonlinearity of the
Heaviside type in the setting of Orlicz-Sobolev space. The presence of both
strongly-singular and non-continuous terms bring up difficulties in associating
a differentiable functional to the problem with finite energy in the whole
space $W_0^{1,\Phi}(\Omega)$. To overcome this obstacle, we established an
optimal condition for the existence of $W_0^{1,\Phi}(\Omega)$-solutions to a
strongly-singular problem, which allows us to constrain the energy functional
to a subset of $W_0^{1,\Phi}(\Omega)$ to apply techniques of convex analysis
and generalized gradient in Clarke sense.
