How can one rebut the argument that atheism is inherently immoral?

It not uncommon to see religious people arguing that without the moral center of a religious text, true ethics are impossible. The reasoning goes that, without a fixed moral center, atheists are free to make up their own beliefs about what is right or wrong. And while the majority of them make the "right" choices, roughly in line with "objective" religious morality, nothing forces them to do so. They could, for instance, adhere to the ethical arguments about stealing being the correct and moral thing to do in cases of extreme inequality. Or, in a more extreme case, justify killing other humans on the basis of their actions or beliefs. Instinctively, this argument feels wrong to me. After all, if it's really that simple, why do so many atheists make the "right" moral choices? And why do some religious people go to great lengths to justify stealing from or killing those of other religions. Yet I cannot formulate this argument into sensible propositions. Is there a good rebuttal?