Bad departmental funding, when do you leave the ship?
Step 0: Document all your efforts to find a solution to this situation. Save a copy of that email from your chair. If you need to resort to Step 4: Hire a Lawyer, a paper trail is invaluable. Also, as @JeffE noted in the comments: stop working until you are paid. This is your most powerful negotiating tool. Don't worry about breach of contract; your employer did it first by failing to pay you.

Step 1: Meet with your immediate supervisor. As a postdoctoral researcher, some/most/all of your salary probably comes from grant accounts, and not the department's general payroll. If there is a financial problem in your department you should still get paid.

Unless, in order to pay you, money has to be transferred from the grant account to the payroll account. This is how it works at my institution. If the payroll account is wonky, then you cannot get paid, regardless of where the money comes from.

Step 2: Meet with your department chair, one-on-one. He/she may be more willing to be forthcoming with the details in a personal setting. There could a rational, if scary, explanation for what is going on. It may be outside of the chair's power. It could be that the department was expecting payments from grants that did not happen. It could be that an allocation from the institution or state or whatever has not arrived due to budgetary problems. If meeting with the department chair is not satisfactory, go on to step three.

Step 3: Contact your institution's central payroll or human resources office. Ask about the situation nicely and politely, but make it clear that you want to know what is going on and when you will be paid. As these folks are either 1) removed from the situation if it is department specific, or 2) closer to it if it is institution wide, you will likely get an answer. Indicate that you believe the department/institution to be in breach of your contract and that you are consulting legal counsel (even if you are not yet). Sometimes, that will grease the wheels.

Step 3.5: Sit tight for a little while and see if it does not go away. If your institution/department does not have a history of such shenanigans, this could be a one-time, but very annoying, blip. Also, look for another job. Be honest with your supervisor about why you are doing so - this financial snafu has you worried about the security of your contract.

Step 4: Hire a lawyer. By failing to pay you per an agreed upon schedule, your employer is in breach of your contract. I would only go this way if you are desperate. 1) The litigation route is likely to take away a large portion of your time that you should be spending doing research or looking for another job. 2) Depending on the ratio of legal fees to missed pay, you might lose money overall. 3) The heavy handed approach may alienate your department, robbing you of recommendations.