Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼ 10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron-phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the (3)He/(4)He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.