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This paper presents analytic study of heat and mass transfer in a two-dimensional, unsteady flow of Maxwell nanofluids over a horizontal stretching sheet. The non-linear governing equations with the relevant boundary conditions have been simplified by using similarity transformations and the resulting equations are solved by using the homotopy analysis method. The convergence and accuracy of the solutions are verified. Impacts of magnetic field, thermal radiation, heat source, surface permeability and chemical reaction on velocity, temperature and nanoparticles volume fraction profiles are examined and presented in graphical and tabular forms. The study reveals that increasing the effect of heat source maximizes the temperature profile whereas it reduces the nanoparticle volume fraction profile in the boundary layer. On the other hand, the increase in chemical reaction is found to enhance the nanoparticle concentration. Keywords:- Homotopy Analysis Method; Unsteady Flow; Boundary Layer Flow; Maxwell Nanofluid