A more common (but still debatable claim) is that with Christianity, religion and philosophy fused in a way that had not before in the west (that is, Greek and Roman pagan theology did not dialog with philosophy in the way that, eg Augustine or Aquinas seemed to work in the overlap between the two).
To answer your question, consider these three examples:
Aquinas's work in general was greatly influenced by Aristotle, as well as his moral philosophy. Obviously, being Christian, he would say something like Aristotle lacked the full knowledge of morality, but his work certainly indicates Aquinas's approval of large parts of Aristotle's morality and ethics.
Augustine discusses the influence of Pagan philosophy on his conversion to Christianity, but in particular looked to Cicero as a hero, frequently citing Hortensius (a work that is unfortunately lost).
It was a particularly thorny problem in Medieval theology and philosophy what to do about Socrates - he was a pagan, but he was also acknowledged as one of the wisest, and therefore one of the most moral, people in history. Aquinas and his teacher, Albert, grappled with this issue.
So, just based on these three data points, it's safe to say that morality is not a Christian invention, given that three prominent Christian philosophers (Augustine, Albert and Aquinas) think otherwise.