Follow-up: Can objective morality exist without God?

In my last question I asked about whether there were any alternatives to moral objectivism and moral relativism and a lot of people commented that they didn’t think that moral objectivism was necessarily associated with God. But can that be? How can moral objectivism exist without God?

I’ve often seen the argument A) Moral objectivity cannot exist without God, B) Moral objectivity exists, thus C) God exists.

The point that bugs me the most is point A. Can moral objectivity exist without God? If so, what would it be founded upon?

Again, not really looking for an atheism vs. theism debate. But as a philosophy minor, this kind of thing comes up sometimes. This isn’t something we were studying outright, but it is something I came across in a book I was reading…just got me thinking…