  In this paper, we deal with the existence of nontrivial nonnegative solutions
for a $(p, N)$-Laplacian Schr{\"o}dinger-Kirchhoff problem in $\mathbb{R}^N$
with singular exponential nonlinearity. The main features of the paper are the
$(p, N)$ growth of the elliptic operators, the double lack of compactness, and
the fact that the Kirchhoff function is of degenerate type. To establish the
existence results, we use the mountain pass theorem, the Ekeland variational
principle, the singular Trudinger-Moser inequality, and a completely new
Br\'ezis-Lieb type lemma for singular exponential nonlinearity.
