We present a simple on-chip electronic thermometer with the potential to operate down to 1 mK. It is based on transport through a single normal-metal–superconductor tunnel junction with rapidly widening leads. The current through the junction is determined by the temperature of the normal electrode that is efficiently thermalized to the phonon bath, and it is virtually insensitive to the temperature of the superconductor, even when the latter is relatively far from equilibrium. We demonstrate here the operation of the device down to 7 mK and present a systematic thermal analysis.