Superconductivity near 30 K was discovered recently in a copper-free phase, Ba 1-x K x BiO 3 (refs 1, 2). This material has structural and electronic properties in common with both the cuprate high-transition-temperature (high-T c ) superconductors and with BaPb 1-x Bi x O 3 , which has a T c of ∼12 K (ref. 4). Here we report the growth and structural characterization of single crystals of Ba 1-x K x BiO 3 . A maximum T c of 30.5 K is found from d.c. susceptibility measurements for crystals of approximate composition Ba 0.6 K 0.4 BiO 3 . The structure for a crystal with x = 0.37 is determined by X-ray diffraction and is found to be a simple cubic perovskite with a = 4.2869 (6) Å. A commensurate lattice distortion occurs for x = 0.04, which is identified as a distortion of the BiO 6 octahedra. Effects of structural distortions and concomitant changes in electronic properties in this non-magnetic system may contain clues to the role of phonons and electronic interactions in the microscopic pairing mechanism of high-T c superconductors.