By quenching the tetragonal phase during flux growth of YBa2Cu3O7-δ, separating the crystals from the flux, and then oxygenating them without mechanical stress, we routinely obtain crystals having untwinned regions. The size of the untwinned regions often approaches that of the crystals, which is typically 1 mm x 1 mm in the a - b plane. Such regions can be cleaved away, yielding isolated untwinned crystals. Unlike thermomechanical detwinning methods, our method does not involve applying mechanical stress to crystals at elevated temperatures. Hence the possibility of introducing stress-induced defects is avoided. Optical microscopy and X-ray diffraction have been used to verify that the crystals are untwinned and of high quality. The crystals consistently show a sharp ( < 2 K wide) superconducting transition near 90 K in the low field (10 Oe) magnetic susceptibility, and exhibit complete diamagnetic shielding in the superconducting state.