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This paper is concerned with the study of a transient hydromagnetic Couette flow and heat transfer of a reactive viscous incompressible electrically conducting fluid between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The transient momentum equations are solved analytically using the Laplace transform technique and the velocity field and shear stresses are obtained in a unified closed form. The energy equation is tackled numerically using MATLAB. The effects of the pertinent parameters on the fluid velocity, temperature, the shear stress and the rate of heat transfer at the plates are presented in graphical form and discussed in detail. Our results reveal that the combined effects of magnetic field, rotation, exothermic reaction and variable thermal conductivity have significant impact on the hydromagnetic flow and heat transfer.