Not long ago I was standing with some friends outside a mosque, handing out literature to Muslims exiting from their Friday service. Things were going well when suddenly a large man came out from the mosque and encountered one of my friends, an older gentleman. The Muslim man said, "You think your God is the right one! I have a challenge for you!," his voice growing louder with each sentence. "This week I challenge you to pray to your God, and I will pray to my God. We both will ask our God to strike dead the one who worships the false God. You meet me here next week at the same time to see whose God is God, if you're still alive!"
My friend was quite taken aback. He did not quite know how to respond. He thought about it for a few minutes and finally agreed they would meet the following Friday at the same time in front of the mosque.
This is a form of the practice known as Mubahala and finds its authority from the Qur'an in Sura 3:61 which says, "But whoever disputes with you in this matter after what has come to you of knowledge, then say: Come, let us call our sons and your sons, our women and your women, and our people and your people, then let us be earnest in prayer and pray for the curse of Allah on the liars."
First, notice a distinct difference here between Islam and Christianity. While the Qur'an, spoken by Muhammad to his people, calls on Muslims to curse Christians, Jesus called on Christians to bless all people, including Muslims, and even to bless those who curse us (Luke 6:28).
Second, note that this practice is not an invention of Islam. It goes all the way back well over 3,000 years to the duel on Mount Carmel between Elijah and the prophets of Baal (1 Kings 18: 17-46). Muslims must be careful who they challenge to a duel. Though we wish no harm on them, you don't mess with the God of the Bible. When challenged, to prove "whose God is God" He eliminated the 450 prophets of Baal along with the 400 prophets of Asherah and sent a strong message. Muslims dare not challenge God this way today or be prepared to face the consequences.
So how did the story end for my friend? He showed up the following Friday but the Muslim man did not. I don't know why. Perhaps God accepted his challenge; perhaps he was just embarrassed that his god was shown to be pitiful and powerless.
But other Muslims have challenged Christians and wish they had not. For such an account, read the story of David Wood being challenged to a Mubahala here.