Thermodynamic Work of a Liquid in Equilibrium with its Vapor

Please explain to me how this statement is true (or not, as the case may be!):

"If we have a liquid in equilibrium with its vapor, the chemical potential of the species must be the same everywhere, and no work is needed in removing a molecule from the bulk region to the surface region"

I am trying to contrast this statement with the true situation that it does require work to move a molecule from the bulk to the surface region, as doing so increases the surface area and therefore the surface energy of the system.

Please be as detailed as possible in your response, using thermodynamic arguments and explaining fully what is meant by the term "work".