  We consider a family of chiral non-Hermitian Gaussian random matrices in the
unitarily invariant symmetry class. The eigenvalue distribution in this model
is expressed in terms of Laguerre polynomials in the complex plane. These are
orthogonal with respect to a non-Gaussian weight including a modified Bessel
function of the second kind, and we give an elementary proof for this. In the
large $n$ limit, the eigenvalue statistics at the spectral edge close to the
real axis are described by the same family of kernels interpolating between
Airy and Poisson that was recently found by one of the authors for the elliptic
Ginibre ensemble. We conclude that this scaling limit is universal, appearing
for two different non-Hermitian random matrix ensembles with unitary symmetry.
As a second result we give an equivalent form for the interpolating Airy kernel
in terms of a single real integral, similar to representations for the
asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes
its structure as a one-parameter deformation of the Airy kernel more
transparent.
