We report on the size and the size distribution of GaAs nanoislands via Ga droplet induced chemical beam epitaxy. GaAs nanoislands were grown by the direct injection of triethylgallium and the subsequent supply of thermally cracked arsine on a nonpretreated substrate. The size distribution of islands as measured by the quotient sigma/d(alpha) the standard deviation of the island diameter (sigma) divided by the mean island diameter (d(alpha)), increases with increasing beam equivalent pressure of triethylgallium but is independent of the total amount of triethylgallium supplied. The influence of annealing was not observed on the size distribution of GaAs islands. These results demonstrate that nanoscale GaAs dots with a narrow size distribution can be achieved by the optimization of growth conditions.