The classic apologetic argument from morality is that if God doesn't exist then objective moral truth doesn't exist. It's often assumed in this argument that somehow God's existence explains morality in a way that atheism cannot. However, this argument mostly focuses on why atheism cannot explain morality, rather than how it is that Christian theology offers a more compelling explanation.
What's more the classic Christian response to the Euthyphro argument is to say that the "good" is that which is like God's nature and character (and because God is unchanging what is good will not change). But how is it that God's character provides the moral foundation for what is good?
I want to suggest that it is the theology of man made in the image of God that not only grounds morality, but also underpins our response to the Euthyphro dilemma. Because we are made in the image of God not only do we have reason to be moral, but what is moral is also that which is like God. But what does it mean to be made in the image of God?
In Genesis God decides "let us make mankind in our image, in our likeness". The traditional understanding of the image of God has been the one filtered through a Greek mindset. A concept which focuses on the abstract and tries to locate what it means to be made in God's image in terms of some property of existence. However, in the last century there has been much study into the concept of the image of God in its original Hebraic context. The Hebraic understanding of man made in the image of God gives a much more functional, and in many ways fuller, understanding of what it means to be human.
Genesis 1 tells the story of God building a temple (the creation of the Earth). It is in the context of this story, and the wider context of the Ancient Near East, that we have to understand what the Bible means in saying we are created in the image of God. Ancient temples would contain "images" of the god for whom the temple was built. Images of gods in temples, or kings in foreign lands, were "viewed as representatives of the deity or king". Kings in Egypt and Assyria were also considered "images" of their gods; meaning that they were ones who "acted on behalf of, and by, the consent of the divine." Middleton points out that typically it was only the king who bore the image of a god, and the concept of all of humanity being made in the image of a god was incredibly counter cultural at the time.
As people created in God's image we are most fulfilled when we reflect God's character, when we act as God would act: according to his character.
The image of God in Western Theology has often been thought of in terms of a mirror reflecting God's likeness back to himself, however a more apt description might be that of an angled mirror reflecting God's likeness to the world itself. The hebraic concept of the image of God tells us that God puts mankind on the Earth as his representatives, that the purpose of man is to show the likeness of God to the world and to live in relationship with him. Obviously we are not successful at this and most of the time we do not accurately reflect God's likeness, which is why most theologians talk of the image of God in us being "marred". The consequence of this, though, is that the closer we come to representing God the closer we come to fulfilling our purpose on this Earth.
As people created in God's image we are most fulfilled when we reflect God's character, when we act as God would act: according to his character. Most meta-ethical theories hold that what is moral is in some way or another what is best for us either individually or communally (either because of the actions themselves or the effects of those actions). So we can see that because we best fulfill our purpose when we reflect God then what it is to be moral is to be act most like God's character. God's character is revealed to us supremely in the person of Jesus: as Wilkinson puts it "Jesus is the decisive norm for both divinity and humanity." If we want to know how best to live as humans we need to look at God, and particularly his actions in Jesus.
This argument serves to do two things. Firstly, we have a simple reply to the so called "dilemma" posed by Euthyphro. Is something good because God commands it or does he command it because it is good. The answer is neither, the good is that which agrees with God's character. And because God's character is unchanging, what is good will also not change, and neither could God ever command anything that is evil.
Secondly, and perhaps more importantly, the fact that we as people are made in the image of God gives us a grounding for morality that atheism cannot. The traditional moral apologetic argument shows us that atheism cannot account for normative morality. However, we can do better than that. Not only can we say that atheism cannot account for morality, but we can show that Christianity can give us a solid foundation for morality. Furthermore, because we are made in the image of God we are living most authentically as humans when we reflect God's character. And here we have a concrete link between what is moral and the character of God. If Christianity is true then not only is there a foundation for morality but we have a clear indication of what it is to be moral in the person of Jesus. What's more Jesus not only shows us what it is to be moral, but by his Spirit he promises to help us in making us more like God. Although God's image in us has been marred Jesus's actions on the cross make a way for that image to be restored in us.
 Genesis 1:26 NIV
 Walton, John, "The Lost World of Genesis One", IVP USA, 2009 Morschauser, Scott, "Created in the Image of God: The Ancient Near Eastern Background of the Imago Dei", Theology Matters, Vol. 3 No. 6, Nov/Dec 1997 - p.2-3
 Wilkinson, David, "The Message of Creation", Inter Varsity Press, 2002 - p.36
 Morschauser, Scott, "Created in the Image of God: The Ancient Near Eastern Background of the Imago Dei", Theology Matters, Vol. 3 No. 6, Nov/Dec 1997 - p.2
 Middleton, Richard, "The Liberating Image: The Imago Dei in Genesis 1", Brazos Press, 2005 - p.100
 Wilkinson, David, "The Message of Creation", Inter Varsity Press, 2002 - p.37