Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties for precision sensing and signal amplification. However, realizing them has remained a daunting experimental task, as non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of non-trivial topology. Here, instead of gain and loss, we use the non-reciprocity of quantum Hall edge states to directly observe non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport measurements evidence a robust, non-Hermitian skin effect, characterized by currents and voltages showing an exponential profile that persists across Hall plateau transitions away from the regime of maximum non-reciprocity. Our observation of non-Hermitian topology in a quantum device introduces a scalable experimental approach to construct and investigate generic non-Hermitian systems.