How secure is a post doc job offer in an email from the department chair prior to receiving the official written letter?
Don't count on an offer until you have it officially, in writing.  A verbal offer is not an offer.  An email or call saying you will get the offer is not an offer.

You say you "emailed the postdoc place".  Who did you email?  If it is an administrator they may not understand the urgency of the situation.  I would email the professor you will be working for and (politely) make it completely clear that you have a non-negotiable deadline for replying to another offer.  You should also state that if you don't have at least a scanned copy of an official offer from him/her before then, you will have no choice but to accept the teaching position, even though the postdoc is your first choice.  If they really want you, they will take the 5 minutes to scan a copy of the letter.  If they don't, maybe it's best to turn down that offer anyway.

In the meantime, I would also negotiate with the second place for an extension of the deadline.