Spontaneous crystallization from a solution in a melt at a pressure of (0.8-1) × 10^-3 Pa was used to obtain single crystals of a new nonperovskite-like superconducting phase Ba₂Cu₃O_6-x (space group P_ccm, a = 13.065, b = 20.654, and c = 11.431 Å). The superconducting properties of the crystals were investigated by modulated microwave absorption. The superconducting transition temperatures were 5 K (sample No. 1), 7 K and 13 K (sample No. 2). The superconductivity in the Ba₂Cu₃O_6-x crystals is attributed to the presence of CuO₂ chains of edge-sharing copper-oxygen squares. Nonperovskite-like Ba₂Cu₃O_6-x crystals are a new class of one-dimensional (1D) superconductors.