  The outlook of protected quantum computing spurred enormous progress in the
search for topological materials, sustaining a continued race to find the most
experimentally feasible platform. Here, we show that one of the simplest
quantum circuits, the Cooper-pair transistor, exhibits a nontrivial Chern
number which has not yet been discussed, in spite of the exhaustive existing
literature. Surprisingly, the resulting quantized current response is robust
with respect to a large number of external perturbations, most notably
low-frequency charge noise and quasiparticle poisoning. Moreover, the fact that
the higher bands experience crossings with higher topological charges leads to
all the bands having the same Chern number, such that there is no restriction
to stay close to the ground state. Remaining small perturbations are
investigated based on a generic Master equation approach. Finally, we discuss a
feasible protocol to measure the quantized current.
