Interviewing for an academic position after abusive department chair in previous academic position In my faculty job, I was bullied for a long time by a chair of the department (at a US state university on the West Coast). This included: 


Giving me bad schedules and classrooms
His secretary telling students to avoid my classes
Denying me operational information
Excluding me from department committees
Falsifying university documents
Stealing my course materials and giving it to his supporters
Filing bogus charges against me that I never saw in writing


I understand it's hard to judge who was in the wrong, but I really had neither motive nor means to fight with the department chair. Worse, he eventually got many of the other department members on his side.

After being bullied and harassed and my working environment sabotaged  for very long time I resigned. Now I am looking for a teaching position at a different university in the USA. I know the number one rule in an interview is “Do not say anything bad about your former employer”. But, under the circumstances, I'm not sure how to answer the question “Why did you leave the position where you achieved a high rank?” What would be a a good way to answer this question?
You can honestly say that the former position was "a bad fit" personally and professionally and that you seek a "more compatible" environment. I've been in enough strange situations that I suspect people are aware that they exist. There are enough similar questions here to indicate that academia isn't utopia. 

You needn't speak ill of the former head. But if the "environment has become less conducive to personal and professional growth" it is likely a fair assessment. 

Also, just having been promoted is an excellent time to "look for other, more challenging, opportunities."