Not to get too legally technical (having passed the Illinois Bar I almost feel that it's my duty to become condescending and obscenely detailed about this topic), but there are a few more legal issues at play.
First, a contract requires an offer, acceptance, and valid consideration (there are other factors, like the capacity of the parties to contract, but those three are the basics). Money-->house satisfies the consideration element.
Second, a verbal contract for the sale of a house wouldn't be upheld because of the Statute of Frauds:
http://en.wikipedia.org/wiki/Statute_of_frauds
Real estate contracts almost always fall under the Statute of Frauds. It's possible some states have different rules, and it's also possible there's some kind of exception in Illinois (I've never dealt with real estate contracts), but the general rule is that they need to be in writing.
Partial performance takes an oral contract (or any non-signed contract) out of the Statute of Frauds and could make the contract enforceable, but no such performance exists in this case.
The more pressing legal issue, however, is whether someone can refuse to sell to a protected class. The Fourteenth Amendment, The Civil Rights Act, and other state, local, or administrative regulations, like the Fair Housing Act, have a long, well-litigated history of asnwering that as, NO!