An "objective moral value" is a moral value that is true independently of whether anybody believes it to be so.
On atheism objective moral values do not exist. It's easy to find atheists who agree with this. For example:
• Jean -Paul Sartre: “It [is] very distressing that God does not exist, because all possibility of finding values in a heaven of ideas disappears along with Him.”
• Friedrich Nietzsche: “There are altogether no moral facts”; indeed, morality “has truth only if God is the truth— it stands or falls with faith in God.”
• Bertrand Russell rejected moral realism and retained the depressing view that humanity with all its achievements is nothing “but the outcome of accidental collocations of atoms”; so we must safely build our lives on “the firm foundation of unyielding despair.”
• J. L. Mackie: “Moral properties constitute so odd a cluster of properties and relations that they are most unlikely to have arisen in the ordinary course of events without an all-powerful god to create them.”
• Richard Dawkins concludes that a universe of “just electrons and selfish genes” would mean “there is, at bottom, no design, no purpose, no evil and no good, nothing but blind pitiless indifference.”
- All quotes cited in Paul Copan, "Ethics Needs God," in Debating Christian Theism, eds. J.P. Moreland et. al., 86.
If, then, objective moral values do exist, atheism is false. It goes like this:
1. If atheism is true, then objective oral values do not exist.
2. Objective moral values do exist.
3. Therefore, atheism is false.
But many atheists do believe in objective moral values. Such as, e.g., the atheist who argues that certain Christian claims are wrong or evil. In cases like this we have atheistic confirmation of the existence of objective moral values. Which, then, supports our second premise and falsifies atheism.
Paul Copan writes:
"Just ask: what should we expect if naturalism is true? Russell , Nietzsche, Sartre, Mackie, and Dawkins are just a few fish in the larger naturalistic pond who recognize naturalism’s inability to generate objective values such as universal benevolence and human rights. Theism has no such problem." (op. cit., 87)