  We evaluate averages involving characteristic polynomials, inverse
characteristic polynomials and ratios of characteristic polynomials for a
$N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary
Ensemble with an external source $\Omega$. Relation to a recently studied
statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see
Y.V. Fyodorov arXiv:1710.04699, is briefly discussed as a motivation to study
asymptotics of these objects in the case of external source proportional to the
identity matrix. In particular, for an associated 'complex bulk/chiral edge'
scaling regime we retrieve the kernel related to Bessel/Macdonald functions.
