Question: "Where does the Old Testament predict the coming of Jesus Christ?"
Answer: There are many Old Testament prophecies about Jesus Christ. Some interpreters place the number of Messianic prophecies in the hundreds. The following are those that are considered the clearest and most important.
Regarding Jesus' birth—Isaiah 7:14: "Therefore the Lord himself will give you a sign: The virgin will be with child and will give birth to a son, and will call him Immanuel." Isaiah 9:6: "For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace." Micah 5:2: "But you, Bethlehem Ephrathah, though you are small among the clans of Judah, out of you will come for me one who will be ruler over Israel, whose origins are from of old, from ancient times."
Concerning Jesus' ministry and death—Zechariah 9:9: "Rejoice greatly, O Daughter of Zion! Shout, Daughter of Jerusalem! See, your king comes to you, righteous and having salvation, gentle and riding on a donkey, on a colt, the foal of a donkey." Psalm 22:16-18: "Dogs have surrounded me; a band of evil men has encircled me, they have pierced my hands and my feet. I can count all my bones; people stare and gloat over me. They divide my garments among them and cast lots for my clothing."
Likely the clearest prophecy about Jesus is the entire 53rd chapter of Isaiah. Isaiah 53:3-7 is especially unmistakable: "He was despised and rejected by men, a man of sorrows, and familiar with suffering. Like one from whom men hide their faces he was despised, and we esteemed him not. Surely he took up our infirmities and carried our sorrows, yet we considered him stricken by God, smitten by him, and afflicted. But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was upon him, and by his wounds we are healed. We all, like sheep, have gone astray, each of us has turned to his own way; and the LORD has laid on him the iniquity of us all. He was oppressed and afflicted, yet he did not open his mouth; he was led like a lamb to the slaughter, and as a sheep before her shearers is silent, so he did not open his mouth."
The "seventy sevens" prophecy in Daniel chapter 9 predicted the precise date that Jesus, the Messiah, would be "cut off." Isaiah 50:6 accurately describes the beating that Jesus endured. Zechariah 12:10 predicts the "piercing" of the Messiah, which occurred after Jesus died on the cross. Many more examples could be provided, but these will suffice. The Old Testament most definitely prophesies the coming of Jesus as the Messiah.