Q. What is the basis?
A. Probably stepped up basis at time of his passing.
The usual rule, for a gift, is that the recipient's basis is the giver's basis (what you father-in-law paid for it). But there is an exception for the gift of his home, where he retained the right to live there ("life estate"). "If you give away an asset and keep a life estate in that asset..... the cost basis of the house is "stepped-up" to the value of the house on date of death [IRC 2036]")
More info: http://www.law.cornell.edu/cfr/text/26/20.2036-1
A life estate does not have to be explicitly established in the deed. Your father-in-law probably had an "implied life estate." If so, that would give you the stepped up basis. There is case law on this.
http://accessiblelaw.org/Documents/LifeEstates-Inheritances.pdf(IRS document)
