Is our building contractor required by law to provide an itemized bill?

The law does not specifically require an itemized bill. If you do not believe or agree with the bill, your recourse is to refuse to pay and  then either settle with the contractor for some mutually agreeable amount, or wait for the contractor to take legal action, at which point you can use the legal process of "discovery" (e.g. subpoenas; interrogatories, which are written questions; notices to produce documents) to obtain information as to cost, to attempt to prove that the bill was unjustified.

Note, however, that by allowing them to do the work without requiring an estimate or proposal, you are in a weak legal position--you likely would have to show not merely that the bill is higher than expected or that it "should" have been, but that the contractor is committing some form of fraud--such as billing you for work not done; billing you more for materials than the materials actually cost--to prevail. You in essence gave the contractor a "blank check" by having him do work without an estimate, proposal, or some maximum cap to cost.