For the first time, the possibility of producing silicene on CaF2/Si(111) substrates modified by electron irradiation is experimentally demonstrated. It is shown that areas of the planar surface of CaSi2 with hexagonal packing formed under an electron beam can be used as a natural template for the subsequent growth of silicene. Silicon is deposited on such surfaces and the formation of silicene islands is confirmed by atomic force microscopy and Raman spectroscopy.