Christians as well as Jews believe that God made the Israelites as his "Chosen People."
Why does God need a Chosen People at all?
The Scripture isn't clear on why, but here are a few suggestions that make sense to me.
God made a lot of choices throughout history and it helps to understand the broader perspective.
The First Man and Woman
He created Adam and Eve 1) in His image, 2) to populate the earth. The results were to be a world full of people in the image of God, worshiping Him, exercising dominion, ruling and bringing things to fruitfulness.
However, Adam and Eve fell, so the image of God in them was now marred to some extent. This culminated at the time of Noah when God was grieved with the evil in the world and that "every inclination of the thoughts of men were only evil all the time." Even though the population had increased significantly and was filling the earth, it was with the wrong kind of people--evil people. God indicates in the judgment of Adam and Eve that an ultimate solution will one day come--the Seed of the woman.
The Man of Favor
Then, Noah chose Noah--a righteous man, blameless among the people of his day. That is the kind of people God wanted to populate the earth. So, God judged the wickedness and started over with Noah, the man of favor.
This failed at Babel when the people refused to be "scattered over the face of the earth", which is specifically what God had commanded. So, God confused their languages to force them to fulfill His command. This fulfilled one part of His divine plan--people were scattering over the earth, but they were people who had to be forced to do so because of their rebellion. So, in order to have a world full of people in the image of God with whom God could enjoy relations, God had to have a plan to reach all people all over the world.
The Man of Faith
Enter Abraham. Although it took many years for Abraham to develop into the man of faith, that was precisely God's plan--that Abraham and his descendants (the chosen people) would ultimately be a blessing to all people (who were now scattered over the whole face of the earth).
Israel also failed to do this fully, although there were considerable successes. Through the Exodus, the Egyptians would know that there was a God in Israel as God answered Pharaoh's question, "Who is the Lord?" Through Daniel, Nebuchadnezzar recognized the God of Israel and even wrote a letter to his entire kingdom proclaiming the greatness of God Most High. Many other examples could be cited. However, ultimately Israel continued to reject God again and again and failed to be His messengers to the whole world. The House of Prayer for all nations became a place restricted to Israelites only, and Jesus Himself cleared the court of the Gentiles that was being used as a market rather than a place for the Gentiles to worship.
Still, in the lineage of Jesus, mention is made of several Gentiles who worshiped the God of Israel (and the world), including Rahab of Jericho and Ruth of Moab. Even Bathsheeba was the wife of Urriah the Hittite.
God's ultimate plan, mentioned in the curse of Adam and the blessing of Abraham (as well as many other places) culminated in the Messiah, as God the Son entered the world through the Virgin Birth, paid the penalty for sins so that men could be forgiven and be indwelt by the Holy Spirit. This would enable men to live more righteously through the power of God.
Jesus final words were a commission to the disciples (now apostles--ones sent out with a message). Their task--to take the gospel to "all the nations of the earth", so that all men may know the one true God and live righteously in relationship with Him.
The Church--now the "chosen people" of God based on faith rather than ethnicity--has certainly had its own share of failures. However, according to Wycliffe, the Word of God will become available to all the languages of the world probably by the end of this century.
The gospel will indeed soon reach all people of the earth. This was the commission to 11 common, ordinary men who dealt with extreme persecution by their own people as well as the Romans. It was quite a bold prediction that one day people from "every tribe, language and people" would recognize Jesus as Messiah in those early days (Revelation 5:9; 7:9). Yet, that is a very probably reality within the next 50-100 years.
So, God chose the people of Israel for a time (about 2000 years) to fulfill His ultimate purpose for all time. Israel succeeded in part, but the ultimate plan was for them to be the people from whom the Messiah would come. The Church was born by the people of Israel. Even now, many Jewish people are recognizing Jesus as their Messiah.