Being harassed by a department chair
I agree with JeffE that leaving is the best solution, but it may not be an option.  One key question is whether you have tenure: if not, you're presumably doomed (if the chair's behavior is as bad as you fear) and you will need to find another job anyway.

Assuming you have reasonable job security, I'd sit down with the chair and ask what he envisions.  Don't complain, argue, or try to present your side.  Instead, you could start by acknowledging that the two of you have unfortunately gotten off to a rough start in your working relationship, and that because of his stature and leadership role it's important for you to earn his respect, so you'd like his advice on how to improve the situation.  Your goal is to learn, not to debate.  Don't explicitly agree to any facts that aren't true, but you don't have to fact check everything he says, and you shouldn't dispute his perspective or opinions in this conversation.

One possibility is that he is an insecure jerk who wants you to submit to his power and authority.  If you do so, and let him boss you around a little without complaining, then he may treat you somewhat better.  [This is assuming he can't treat you any worse than he already is.  If you fear things could get worse, then be careful, but your question suggests you don't have a lot to lose.]

Another possibility is that he just doesn't want you around, and there's simply nothing you can do to get on his good side.  In that case, maybe he could help you transfer to another related department, for example.  Of course, you can't even bring this up unless you have some job security, since otherwise you have no leverage at all.  And it's important to do it in a face-saving way.  There's no way it will happen if it looks like he is getting rid of a problem employee (the administration and the other department will not accept that as a valid reason for such a transfer), and obviously he won't cooperate if the stated reason is getting you out from the control of an irresponsible chair.  Instead, you'd have to give it a positive spin: helping your career by giving you a chance to develop in a slightly different research direction, building ties between departments and fostering interdisciplinary connections, etc.  It may be galling, but you need to set this up in a way that makes it look like your chair is doing something valuable for the university by helping to arrange it.  If you can get your chair enthusiastic about this, and if there's another plausible department, then the chair's influence within the university might really help you.  And don't be too restrictive in ruling out possible departments: there might not be any appropriate match, but I know of a couple of cases in which people have successfully resolved personality conflicts by moving to departments that were a bit further afield than one might expect (engineering vs. science, for example).  If you've got tenure, then the university has a powerful incentive to fix this conflict, even if it means letting you sit in an odd department.

Leaving the university is radically different from switching departments, and you should not ask the chair for help in doing that.  Within the university, your chair's standing with the administration will play a major role in what opportunities are available.  Outside the university, your chair probably can't help you very much, but could certainly hurt you, so it's not worth the risk.

The worst case scenario is that your chair hates you and wants to hurt your career, regardless of which department you are in.  In that case, there's nothing you can do if your chair has the full support of the administration, and you'll have to either leave the university or wait for the chair to retire.  However, you shouldn't give up all hope until you've exhausted options like submitting or transferring.