The possibility of measuring the scale parameter of quantum chromodynamics, Λs, at CHEER is discussed. Rationale for the measurement of this quantity are given, along with a discussion of the theoretical difficulties involved. The measurement of the Q2 dependence of structure functions and their moments, and methods of measuring αs and its Q2 evolution, are discussed, and arguments are given for the advantages and disadvantages of going to high Q2 values at CHEER. It is concluded that while sensitivity to Λ is lowered at high Q2, CHEER will, in principle, be able to provide the first clean measurements of Λ, free from almost all the theoretical confusion involved in interpretations of present data.