I did a BS in Mechanical Engineering and am now finishing my MS in Chemical Engineering. I did not have to do any extra courses but I did need to do a lot to catch up for some courses (Reactions/Catalysis and Thermodynamics). You will have a lot of trouble if you did not take some undergraduate ChemE courses. From the ChemE courses I have taken, Organic Chemistry and Chemistry, are not important. Fluid Mechanics, mass transfer, heat transfer, and thermodynamics are more important.