Actually whatever you presented here would be construed as a contract by the judge. This "contract" is a perfect example of what not to do for house repair, rebuild, remodel because it leaves everything wide open, not for you, but for the contractor. It did not define the dimensions, shape, etc. of the chimney. It did not require what brand of materials for the rebuild, and how much. Worse, it did not define the quality of the work or the liability for the contractor if anything happens to the chimney due to lack of quality in the future. it did not define when the work should be completed.
Your only chance to win over the contractor is to get the worker to put something in writing (affidavit: a signed written testimony) that the contractor did not rebuild the chimney. If so, you can negotiate with the contractor's lawyer to reduce the costs and a leverage against the contractor to take this matter further.
