Typically, an atheist will ask, “Why can’t an atheist know and do good without God?” The usual (and quite helpful) response is that, yes, atheists can know and do good without acknowledging God in their lives. However, the main point is the foundation or grounding of the good—and that is plausibly not anything other than God. While this response is adequate, and frames the debate in terms of ontology rather than epistemology, I want to focus a bit on the epistemological claim. I want to say, as a word of warning, that I mean no offense to any atheists, skeptics, agnostics, or non-Christians. If you can read this in a spirit of charity, you may be able even to agree with what I am saying!
I happen to think the atheist often does not, in fact, know his moral obligations and duties. Further than this, there are some moral obligations that bear upon him that he cannot know, even in principle, if God is excluded from the moral epistemology. Now, in a certain sense, no atheist can escape God from his moral epistemology. This is because, as a part of our design, moral knowledge is built in a priori, as a function of how we are to operate. With God as the designer and giver of the moral law, humans everywhere will, if operating correctly, apprehend the moral law.
I hold to a divine command theory of ethics. This means that our moral obligations are constituted by God’s commands. These commands are given in part through the deliverances of a properly functioning conscience. Many of them, however, are deduced from God’s Word. It should strike the reader as obvious that atheists do not accept the Bible as the Word of God. In that case, it just follows that there are some commands that are incumbent upon humanity that the atheist will not even recognize.
Take the example of doing all to the glory of God (cf. 1 Cor. 10:31). For more than one reason, this is not something that immediately shows itself in the consciences of people a priori. It strikes even “veteran” Christians as an insight of morality that each and every aspect of their lives, even down to what they eat or drink, is to be consecrated to God. It then becomes obvious that atheists do not know this moral command, and thus a crucial point of moral obligation is not a part of the atheist’s moral epistemology.
Moreover, as odd as the claim that atheists cannot, even in principle, know certain moral obligations upon them is, we actually see myriad examples in everyday life. Consider the fact that atheists and Christians are at odds on a great many moral issues. Abortion, euthanasia, gay marriage and homosexual behavior, raising children, etc. All of these issues exhibit a great controversy between atheists and Christians. Yet Christians derive these moral commands (both obligations and prohibitions) either directly or indirectly from Scripture, coupled with moral intuition. In some cases, it is either not possible or very weak to make a case for certain of these positions on an atheistic epistemology. So I think it follows as obvious there are some positions that, given atheist commitments, are impossible for atheists to know. In that case, it follows they do need God for their moral epistemology.
One final application to make: this applies not only to atheists, but even (in certain cases) to all non-Christians. This is not meant to show that God exists. It is just an interesting avenue to explore, as entailments of my personal positions.
 I do understand, of course, that there are psychopaths, who do not perceive moral right and wrong. This is obviously not the norm.
 I am using “know” here in the sense of “justified true belief.” Presumably, the atheist does not believe God exists, and so does not believe he has the moral obligation to fulfill this command, even if he is aware the Bible teaches it.