InAs quantum dots in a GaAs matrix have been prepared by molecular beam epitaxy using a self-organizing mechanism. A narrow size distribution of single dots of pyramidal shape (typically with a base of 12 +/- 1 nm and a height of 4-6 nm) is created as directly imaged with plan-view and cross-section transmission electron microscopy. The dots exhibit self-organized short range order and preferentially align in rows along [100]. The photoluminescence of the dot ensemble has, due to fluctuations in dot size, shape and strain, a FWHM of typically 50-60 meV. However, using highly spatially and spectrally resolved cathodoluminescence it is possible to directly excite a tiny fraction of all dots (typically only 30 dots). Under these excitation conditions the spectrum changes drastically into a series of ultrasharp lines with a FWHM < 0.15 meV, each originating from a different single InAs quantum dot. This directly visualizes their delta function-like density of electronic states, especially since the lines remain sharp even for k(B)T much greater than FWHM.