I own a residential remodeling company, S Corp. Can I contract the company to build my own new home?

Sure. That is assuming the owner (you only I presume?) has a valid active contractors license to build an entire home from the foundation to the roof. While you very well may have such a license, I myself don't know any "remodeling" companies that are licensed for top to bottom construction. Folks generally use a building contractor for that.
If you are a W-2 employee of the S-Corp I would recommend that you not pay yourself as an employee for any work that you may do on your house in the process. Otherwise, you'll find yourself paying taxes on your money twice.
You will be paying the S-corp with money you have already paid taxes on. Then the S-Corp will be paying you a wage for the work you do on the house, and that wage income reported on your W-2 will be taxable income to "you" again.

Thanks for answering.   

The majority of remodeling contractors i know hold full residential builder licenses like i do.

Carl, in Illinois and other states contractors are not required to be licensed.

Yep, each state is different. But it still doesn't change the money flow. So you want to be careful about paying yourself as a W-2 employee for work on your own property, so you're not paying taxes on your own money twice. Basically, instead of say, your standard 20% markup for materials, you may only do a 1% (if any at all) markup to cover delivery costs and the such.

Thanks for the reply, Carl.  I am using my employees on payroll for the work.  Company will show reasonable profit in line with it's other business contracts.   My accountant seems to think the idea of my contracting my own business for my personal project is illegitimate by double dipping, but it's not double dipping when I'm paying the Company from my own personal after-tax money and company will make a normal and reasonable profit on which it will pay state and federal income tax.  

Maybe I need a new accountant...

I guess I don't understand the purpose of hiring your company, versus you just personally hiring the contractors yourself.

Depending on what exactly happens on the tax returns, if there is any tax savings due to hiring your own company, I agree with the accountant, it would not be allowed.  However, there may not be any tax savings (depending on exactly how you are doing it), in which case it would be okay (but as I said before, I don't understand the purpose of it).

@m.vesey I am not an accountant, CPA, Tax Attorney or anything else that would qualify to anything close to an expert on this stuff. I am just another user exactly like you. Now like you, I too am self-employed but with my own single member LLC. While I am aware of some of the laws, rules and regulations concerning other types of business structures such as an S-Corp, I am by no means "qualified" to advise on it in a legal sense of the word. When it comes to S-Corps, there are a few facts that I "know", such as the requirement to take a minimum draw each year. But how that minimum is determined, I'm clueless.
Now TaxGuyBill is a retired CPA, accountant, or something like that I think. So he knows more about that S-Corp stuff than I do. But overall, I would go with the accountant you are paying for the advice, because that's someone you can possibly hold legally liable and financially culpable for the advice they give you. You don't have that sort of "cover" in this public user-to-user forum.
One thing you can do in this forum, is click on the screen name of any participant and read their profile. I don't think TGBill has a profile. But I do. For me, it will give you an idea of my experience and knowledge. But even then, that doesn't make me an expert on anything.

Thanks TaxGuyBill.  I won't see any lessening of taxes due, but I have my own crew on payroll and I want to hire my own Corp to do the work.