  We investigate the Hall conductance of a two-dimensional Chern insulator
coupled to an environment causing gain and loss. Introducing a biorthogonal
linear response theory, we show that sufficiently strong gain and loss lead to
a characteristic non-analytical contribution to the Hall conductance. Near its
onset, this contribution exhibits a universal power-law with a power 3/2 as a
function of Dirac mass, chemical potential and gain strength. Our results pave
the way for the study of non-Hermitian topology in electronic transport
experiments.
