Using a regular perturbation technique, an analytical solution is reached for laminar flow mass transfer in hollow fibers containing a chemical reaction. Specifically, the nonlinear boundary condition resulting from the heterogeneous chemical reaction is expanded in an infinite series. This motivates the perturbation technique used to recast the nonlinear system into a series of linear systems. Analytical solutions to some of these linear systems have been published. This result is useful in evaluating the enhancement in separation that is obtainable in facilitated membrane processes.