In the New York Times magazine a psychology researcher, Paul Bloom, has published a report of research into some signs that very young children show some inklings of a moral sense, distinguishing between mean and nice actions and preferring the latter to the former.
I'm afraid I can't agree with Bloom's conclusions. The article gestures at psychological research which shows that babies sometimes predictably and spontaneously behave in ways we'd expect moral beings to. There are two large problems it doesn't address: which responses are supposed to count as moral and why; and, how the sentiments which underlie the babies' actions are supposed to relate to morality as a whole.
On the first point: why should we take those baby responses to be moral ones? For instance, the studies record the babies' interests by tracking their eye movement. But by that measure, babies prefer human faces (and other objects) with symmetrical features, or anthropomorphic figures to non, in just the same way they prefer 'nice' to 'mean' actions. You and I know that the first group are aesthetic rather than moral preferences, but we have reason to believe the babies don't (and no reason to believe otherwise). Making these types of distinctions is crucial to moral action (though we need not conclude from that, as many have, that moral preferences have no links to non-moral ones). Secondly, whatever morality is, it is not just the expression of sentiments. There are sentimentalist moral theories which are serious candidates (Michael Slote's comes to mind), but even in them there is a lot of ground to cover between having a sentiment which is broadly compatible with moral action, and having a moral life. For one thing, there must be some way to seperate the appropriate sentiments from the inappropriate ones. And we have no reason to believe that children, even well past infancy, are able to do so.
The conclusion that there is some, if even a rather impoverished, moral life at work with babies is likely to be a case of the over-analysis of results. The quickest way to point this out is to gesture at a confusion and its converse. It is a mistake to believe that if babies (or anyone else) doesn't have a moral life, properly construed (whatever that turns out to be), that no action they take would be moral. This is like believing that because dice themselves can't know or care how they land, they will never roll the numbers we like. The article goes the other way: because babies act in ways we see as moral, they actually are moral, at least in some way. But it is quite likely that babies would occasionally do things we would look upon as moral, even do so reliably and spontaneously, for reasons of their own. That is, for non-moral reasons. And that possibility is never discussed in the article.