How do I force one record to have a true value for a boolean column, and all others a false value?
Note: This answer was given before it was clear the asker wanted something MySQL specific. This answer is biased towards SQL Server.

Apply a CHECK constraint to the table that calls a UDF and makes sure its return value is &lt;= 1.  The UDF can just count the rows in the table WHERE isDefault = TRUE.  This will ensure that there is no more than 1 default row in the table.

You should add a bitmap or filtered index on the isDefault column (depending on your platforom) to make sure this UDF runs very quickly.

Caveats


Check constraints have certain limitations.  Namely, they are invoked for every row that is modified, even if those rows have not been committed yet in a transaction.  So if you start a transaction, set a new row to be the default and then unset the old row, your check constraint will complain. That is because it will execute after you make the new row the default, find there are now two defaults, and fail. The solution then is to make sure you unset the default row first before setting a new default, even if you are doing this work in a transaction.
As gbn pointed out, UDFs may return inconsistent results if you are using snapshot isolation in SQL Server.  However, an inline UDF does not run into this issue, and since a UDF that just does a count is inline-able, this is not an issue here.
The strength of a database engine's processing power is in its ability to work on sets of data at once.  With a UDF-backed check constraint, the engine will be limited to applying this UDF serially to every row that is modified.  In your use case it is unlikely that you will perform mass updates to the PostalCodes table, however this remains a performance concern for those situations where set-based activity is likely.


Given all these caveats, I recommend using gbn's suggestion of a filtered unique index instead of a check constraint.