When hiring an Enterprise Architect (EA), what is most important for them to have on their CV?

Depends on which kind of role in my EA organization I am filling, but in some cases, industry knowledge is very important (if in a "true" Enterprise Architect / Strategic Architect or business aligned architect role).  In other cases, such as solving for a more technical / Solution Architect-type role, general EA knowledge can be more important. A good Enterprise Architect should be able to operate in nearly any kind of technology:business alignment need or opportunity, and quickly sort out what is important and required for it, bringing the right people together and "framing the debate" for the options to move forward.  In many cases, this is where an EA adds value, at a minimum putting an objective, strategic process into place to help drive a desired outcome, balancing the tactical and the strategic needs of an organization.