A scanning force microscope with a base temperature below 300 mK is used for measuring the local electron density of a two-dimensional electron gas embedded in a Ga[Al]As heterostructure. At different separations between atomic force microscope tip and sample, a dc voltage is applied between the tip and the electron gas while simultaneously recording the frequency shift of the oscillating tip. Using a plate capacitor model, the local electron density can be extracted from the data. The result coincides within 10% with the data obtained from transport measurements. (C) 2003 American Institute of Physics.