Nanocrystallites of GaAs have been prepared by refluxing GaCl3 with As(SiMe3)3 in decane at 180-degrees-C for 72 h. The crystallites formed have an average diameter of 3 nm. Controlled growth of these crystallites to a desired average diameter is possible by autoclaving at 200-degrees-C. Changes in the measured optical absorption spectrum associated with this ripening process are described. Spectral features in the 400-550-nm region, previously assigned to molecular species in solution or adsorbed at the surface of GaAs crystallites, are absent. Optical absorption bands at 302 and 314 nm, observed for GaAs crystallites whose average diameters are 3 and 4 nm, respectively, are tentatively assigned to the 1S-1S transition. The observed absorption onset is compared with that predicted, using the effective mass approximation and pseudopotential methods, for spherical crystlalites of the appropriate diameter. Agreement of the measured onset for absorption with that predicted on the basis of the effective mass approximation is excellent. However, for crystallites whose diameter is less than about 5 nm the observed blue shift is smaller than predicted. Implications of these observations are discussed.