The unsteady free convection flow of a viscous incompressible stably stratified fluid past an infinite vertical oscillating plate with variable temperature and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The plate temperature as well as the concentration level near the plate is raised linearly with respect to time. The non-dimensional governing equations are solved in closed form by the Laplace’s transform technique, when the plate is oscillating harmonically in its own plane. The effects of different parameters like phase angle, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, stratification parameter, and time on velocity, temperature, concentration, skin-friction, Nusselt number and Sherwood number are studied.