God chose to save elect individuals, not the nation of Israel as a whole. He chose the ethnic nation of Israel as a whole to be a light to the world, to receive the Law, and to act as the bloodline for the Messiah. However, this corporate election granted earthly and covenantal privileges, not automatic eternal life.
From eternity past, God unconditionally chose specific, individual people out of fallen humanity (both Jews and Gentiles) to receive saving grace, faith, and eternal life.
Paul states in Romans 9:6 that "they are not all Israel who are of Israel." This means there is a faithful, saving "remnant" within ethnic Israel. God's choice is based purely on His sovereign mercy (as seen in choosing Jacob over Esau before they had done anything good or bad), not on national identity or human effort.
There is one "Olive Tree", rather than two completely separate plans, God's people as one continuous entity, often called the "Israel of God." In Romans 11, Paul uses the illustration of an olive tree to explain this. Unbelieving, non-elect Israelites are "broken off" the tree for their lack of faith.
Therefore, the ultimate chosen people of God—the Church—consists of the total number of the elect from all generations, regardless of their ethnic background.