A solid solution of the quasi one-dimensional cuprate, (Ca1-xYx)0.82CuO2 (0 ≤ × ≤ 0.435), has been successfully synthesized in an oxygen stream at room pressure. Structural changes have been determined for the basic crystal structure by means of the Rietveld method using powder X-ray diffraction. Upon Y doping, the nearest (intrachain) Cu-Cu distance increases from 1.93 to 1.98 Å, while the next-nearest (interchain) Cu-Cu distance decreases from 3.46 to 3.41 Å. The incommensurate superstructure, originating from differences in the periodic arrangement of the (Ca, Y) atoms and CuO2 chains, has also been examined. The modulation period along the crystal a axis implies that the stoichiometry of the solid solution shifts toward that of the cation-deficient member (Ca1-xYx)0.80CuO2. This compositional discrepancy might be canceled by the large change in the modulation period along the c axis.