The Euthyphro dilemma comes from Plato’s Euthyphro dialogue, which has had different forms over the centuries. Basically, it is “Are moral acts willed by God because they are good, or are they good because they are willed by God?" Another way of saying it is, does God say that things are moral because they are by nature moral, or do they become moral because God declares them to be?
The dilemma is that if the acts are morally good because they are good by nature, then they are independent of God and morality somehow exists apart from God. These acts would already be good in themselves and God would have to appeal to them to "find out" what is good. Of course, This raises questions on how moral absolutes can exist as independent abstract entities apart from a divine being. On the other hand, if something is good because God commands that it is good, then goodness is arbitrary and God could have called murder, good, and honesty not good. The problem here is that it means God could also be a tyrant if he so chose to be. But, he chooses to be nice.
Responding to the Euthyphro Dilemma
The Euthyphro dilemma is actually a false dichotomy. That is, it proposes only two options when another is possible. The third option is that good is based on God’s nature. God appeals to nothing other than his own character for the standard of what is good, and then reveals what is good to us. It is wrong to lie because God cannot lie (Titus 1:2), not because God had to discover lying was wrong or that he arbitrarily declared it to be wrong. This means that God does not declare something to be good (ignoring his own nature) or say that something is good by nature (recognizing a standard outside of himself). Both of these situations ignore the biblical option that good is a revelation of God's nature. In other words, God is the standard of what is good. He is good by nature and he reveals his nature to us. Therefore, for the Christian, there is no dilemma since neither position in Euthyphro’s dilemma represents Christian theology.