Abstract The ballistic conduction through narrow constrictions connecting charge reservoirs exhibits conductance quantization effects. Since the quantum of conductance is only related to fundamental constants of nature, these effects might allow the implementation of a standard of resistance, fulfilling the requirements of the 2019 revised International System of Units. Moreover, this standard would be able to work at room temperature and without a magnetic field, thus allowing its on‐chip implementation. In this work, the authors propose that breakdown filaments in thin oxide layers might be useful to this purpose. In particular, conductance quantization effects in nanolaminate Al 2 O 3 /HfO 2 dielectrics are reported and the role of intrinsic values of conductance and extrinsic parasitic elements are analyzed. The fact that breakdown filaments are irreversible is an advantage due to their expected stability and to the lack of cycle‐to‐cycle variations (as compared to resistive switching devices). Although the reported sample‐to‐sample variations are still too large for a real application, there is room for improving the controlover breakdown filaments through material design and electroforming conditions. Provided that this control is achieved, an on‐chip implementation of a resistance standard for the realization of self‐calibrating electrical systems and equipment with zero‐chain traceability would be possible.