We report the detection of the satellite 18 cm OH lines at 1612 and 1720 MHz in the z = 0.24671 molecular absorption system toward the radio source PKS 1413+135. The two OH lines are conjugate; the 1612 MHz line is seen in absorption while the 1720 MHz line is seen in weak maser emission of equal but negative optical depth. We do not detect the main 18 cm OH lines at 1667 and 1665 MHz down to 1.1 mJy rms in 4.0 km s(-1) channels. The detected and undetected 18 cm OH lines support a scenario of radiatively pumped stimulated absorption and emission with pumping dominated by the intraladder 119 mum line of OH, suggesting a column density N(OH) similar or equal to 10(15)-10(16) cm(-2). Combined with simultaneous H I 21 cm observations and published CO data, we apply the OH redshifts to measurements of cosmic evolution of the fine-structure constant (alpha = e(2)/fc). We obtain highly significant (similar to25 sigma) velocity offsets between the OH and H I lines and the OH and CO lines, but measurements of alpha-independent systematics demonstrate that the observed velocity differences are entirely attributable to physical velocity offsets between species rather than a change in alpha. The OH alone, for which conjugate line profiles guarantee that both lines originate in the same molecular gas, provides a weak constraint of Deltaalpha/alpha(0) = (+0.51 +/- 1.26) x 10(-5) at z = 0.24671. Higher frequency OH line detections can provide a larger lever arm on Deltaalpha and can increase precision by an order of magnitude. The OH molecule can thus provide precise measurements of the cosmic evolution of alpha that include quantitative constraints on systematic errors. Application of this technique is limited only by the detectability of \tau\ similar to 0.01 OH lines toward radio continuum sources and may be possible to z similar to 5.