We report for the first time, the synthesis and X-ray diffraction studies of single crystals of BeF2. The crystals were obtained during the sublimation of amorphous BeF2 under static reduced pressure. BeF2 crystallizes in the chiral trigonal space group P3(1)21. A single-crystal X-ray diffraction study on these crystals shows that each of the Be atoms is bonded to four F atoms, and each of the F atoms is bonded to two Be atoms with associated Be-F bond distances of 1.5420(13) and 1.5471(13) angstrom, showing an almost regular tetrahedron. The infrared spectrum of these crystals recorded at room temperature shows distinct peaks around 770 and 410 cm(-1).