We have developed a novel method to fabricate self-assembled quantum dots (QDs) of compound semiconductors on a Si(111) substrate using the so-called 'droplet epitaxy' technique. In order to fabricate QDs on a Si substrate by droplet epitaxy, we examined the termination of a Si (111) surface with a bilayer-GaSe. This surface is formed by depositing I monolayer Ga on a Si(111)-7x7 surface and annealing in a Se flux at 520 degreesC. Then Ga atoms are deposited to form Ga droplets on this surface, and the sample is annealed in an As flux to transform Ga droplets into GaAs QDs. It is revealed that GaAs QDs with a diameter as small as 10 nm and a height of 5 nm can be formed on the bilayer-GaSe/Si(111) substrate at a maximum density of 8.4 x 10(10) cm(-2). Using this method a new technique will be available to fabricate QDs of many kinds of compound semiconductors on the Si(111) substrate.