Quantum Hall systems host chiral edge states extending along the one-dimensional boundary of any two-dimensional sample. In solid state materials, the edge states serve as perfectly robust transport channels that produce a quantized Hall conductance; due to their chirality, and the topological protection by the Chern number of the bulk band structure, they cannot be spatially localized by defects or disorder. Here, we show experimentally that the chiral edge states of a lossy quantum Hall system can be localized. In a gyromagnetic photonic crystal exhibiting the quantum Hall topological phase, an appropriately structured loss configuration imparts the edge states’ complex energy spectrum with a feature known as point-gap winding. This intrinsically non-Hermitian topological invariant is distinct from the Chern number invariant of the bulk (which remains intact) and induces mode localization via the “non-Hermitian skin effect.” The interplay of the two topological phenomena—the Chern number and point-gap winding—gives rise to a non-Hermitian generalization of the paradigmatic Chern-type bulk-boundary correspondence principle. Compared to previous realizations of the non-Hermitian skin effect, the skin modes in this system have superior robustness against local defects and disorders.