Dispensationalists like to throw around the term "Replacement Theology" in their diatribes against the classical Reformed framework, called Covenant Theology. In its simplest form, Covenant Theology is the belief that God has always had His Church, i.e., His elect people. In the Old Testament, this elect community was comprised mostly of Jews. In the New Testament, it is comprised of men and women from all nations. Hence the Dispensationalist label, "Replacement" Theology" is actually a libel. Nowhere is it ever asserted that the New Testament Church replaces Israel as God's chosen people. Rather, God's chosen people have been expanded beyond the boundaries of national Israel.
In my opening sentence, I mentioned that this is the classical Reformed theological framework. But truth be told, it is much older than the Reformation era.
It is quite clear that most of the Apostolic Fathers (the first generation of Church leaders and theologians after the death of the Apostles) saw the Church as the inheritors of the Old Testament prophetic promises. This, of course, is in keeping with what Paul writes in Galatians and Romans 4. The early Fathers clearly believed that they were keeping in line with the doctrine of the Apostles by understanding the Old Testament prophecies this way. This belief continued to be the norm of Christian thought until the rise of John Nelson Darby. Darby, as you may know, is the founder of the modern dispensationalist scheme of interpretation.
Here are a few sample of early patristic thought in this regard:
Justin Martyr writes: "Since God announced he would send a new covenant...we will not understand this of the old law and its proselytes, but of Christ and his proselytes, namely us Gentiles."
Irenaeus writes: "'But...the King has actually come...and has bestowed upon men the good things which were announced beforehand...By his advent he himself fulfilled all things, and still does fulfil in the church the new covenant foretold by the law."
Hippolytus, commenting on a passage in Isaiah says, "For it is not of the Jews that he spake of old, nor is it of the city of Zion, but of the church."
Even earlier than these, we find Clement of Rome exhorting the Corinthian church to humility and unity by an appeal to the lives of the saints and marytrs. Yet, who does he refer to? Abel, Noah, Abraham, Lot, Joseph, Moses and David. Then, to drive home his point, he points to his own day and the martyrdom of Peter and Paul.
The whole arguement of chapter XIII of the Epistle of Barnabas is that the Church, not national Israel, is the heir of the covenant God made with Abraham.
Familiarity with Church History serves as a corrective and precaution against error. Had the Christians of yesteryear been familiar with the standard Christian understanding of Old Testament prophecy, Dispensationalism would never had gotten off the ground.