  Cooling nanoelectronic devices below 10 mK is a great challenge since thermal
conductivities become very small, thus creating a pronounced sensitivity to
heat leaks. Here, we overcome these difficulties by using adiabatic
demagnetization of \emph{both} the electronic leads \emph{and} the large
metallic islands of a Coulomb blockade thermometer. This reduces the external
heat leak through the leads and also provides on-chip refrigeration, together
cooling the thermometer down to 2.8$\pm$0.1 mK. We present a thermal model
which gives a good qualitative account and suggests that the main limitation is
heating due to pulse tube vibrations. With better decoupling, temperatures
below 1 mK should be within reach, thus opening the door for microkelvin
nanoelectronics.
