Hydrogen and Helium are elements, I guess it depends on what your definition of a chemical is.
The reason I'm saying plasma is not a chemical is because it is too energetic to make atom to atom bonds which I feel is the basis for chemistry. If something cannot interact chemically I feel we should not consider it a chemical.
Please note that I did not look up any formal definitions, just expressing my reasoning for my argument. (Aka I'm probably wrong).
You make a good point. I should have said "things in the plasma state" should not be considered chemicals.