The transfer of chemically reactive species in the laminar flow over an elastic plane surface is considered. The viscous flow is driven solely by the linearly stretched surface and the reactive species is emitted from this sheet and undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. A similarity transformation is devised, which reduces the concentration conservation equation to an ordinary differential equation. An exact analytical solution due to Crane [Z. Angew. Math. Phys. 21, 645-647 (1970)] is adopted for the velocity, whereas the concentration field is obtained numerically. The computations showed that the principal effect of a destructive chemical reaction is to reduce the thickness of the concentration boundary layer and to increase the mass transfer rate from the stretching sheet to the surrounding fluid. This effect appeared to be more pronounced for a first-order reaction than for second- and third-order reactions. A nonuniqueness of the concentration distributions for generative first-order reactions was revealed by the computations.