Of course, I cannot speak for any other Greek Organizations but LXA, We do require a Chapter Advisor.
It has seemed to work by getting a Member of the Faculty as an Advisor for two reasons.
1. To have a friendly voice on board with ins above the Undergrad level with the Adm.
2. Having a person older and wiser who could be Initiated as a Member.
Our last two were Faculty, one was not Initiated, the last one was and now His Son is also His Brother!