You have to tell me of a moral statement that can be made by a believer, or a moral action undertaken by a believer, that I couldn't undertake because I am an atheist.
He claims to have never heard an acceptable answer to this question.
I'm afraid I think his challenge is somewhat fallacious, and in fact, the very first time I heard him issue this challenge, one of the theists whom he was debating gave a pithy and perfect response: Tithing.
Now, I believe, and Hitchens certainly believes, and probably most readers of this blog believe, that paying a compulsory or coerced tithe to a religious organization, particular one with "morals" like those that tend to ask for big tithes, is an immoral action. I have asked my wife not to mention anymore the observation that my Mormon parents have spent something like twenty times as much money this year donating to a hate group than they have on gifts for their grandson, because it's too enraging to contemplate.
But that's because we are evaluating the morality of this from a secular perspective. From a theistic perspective, tithing is perfectly moral. And so, duh, that's why a believer would undertake this action and a nontheist wouldn't.
Now, as I have blogged about before, I do not accept relativist justifications for religious buffonery, and in fact I believe in a non-arbitrary basis for morality that may even transcend our species. I think that paying tithing to LD$ Inc., for example, is objectively immoral, so in that sense, it may not technically satisfy Hitchens' challenge.
However, it does undermine the rhetorical power of it, because the entire purpose of his challenge is to "prove" that religion casts no light on morality. But in this sense, his challenge is a tautology. If we already accept that morality must be evaluated in secular terms, then yes his challenge cannot be met, but so what? Yet if we are coming from a perspective where religion does illuminate morality, then it is trivial to meet his challenge.
Really, all Hitchens has done is restate the Evidential Problem of Evil in a weaker form. In my opinion he ought to retire this argument, because it really doesn't do anything for the nontheist/anti-theist case.