I am no expert on the historical question here, but I remark that an adherent of Christianity may have motives other than the obvious for spreading the idea that morality as generally understood is a Christian creation, and that Anscombe was certainly a Christian and I suspect Chappell is too. (And on the other hand a philosopher who doesn't share their religion may have other motives for not being convinced.)
Cautiously weighing in on the historical question despite my non-expertise, here is a brief quotation from Plato's Euthyphro:
But tell me, Euthyphro, do you really believe that you understand true ruling of the divine law, and what makes actions pious and impious, that in the circumstances that you describe you have no misgivings?
Unless this is a severe mistranslation, it seems to indicate a concept of ethics in terms of (1) actions rather than just character and (2) a moral law, which is exactly what Anscombe and Chappelle age saying the ancient Greeks didn't have. On the other hand, as Anscombe says this is about a specific defect, namely impiety -- though Socrates's argument, aiming to show that piety can't mean simply "what the gods like", seems to me to suggest that Plato was thinking more broadly, and indeed the same translation quoted above also has Socrates asking this:
Now consider whether it doesn't seem to you that everything pious must be morally right.
He isn't claiming that the two are the same; a little later he goes on to suggest that piety is one variety of "moral rectitude" and to inquire just what sort. There's at least a hint of virtue ethics in what he says about this, but the impression I get is not that virtue ethics was the only sort anyone understood, but rather that Plato's Socrates is something of a virtue ethicist unlike many of the people with whom he argues.
Unless this is a severe mistranslation, it seems to indicate a concept of ethics in terms of (1) actions rather than just character and (2) a moral law, which is exactly what Anscombe and Chappelle age saying the ancient Greeks didn't have.
I'm not familiar with the context of the quote, but it talks about a divine law, not a moral one. Today most people hold that the two are distinct: for instance if a divine law orders a fasting day, disobeying it is not a moral failure. (Otherwise morality would be indistinguishable from piety and obedience, and we wouldn't need a separate word.)
I was stunned to read the accounts quoted below. They're claiming that the notion of morality - in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.
I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.