What is the history of the "Church of Christ?"

The true history of the church is found in the Book of Acts in your Bible. However, I assume by your question you are wondering about the history of the churches of Christ in the United States. A really good and detailed account is given in a series of books called The Search for the Ancient Order by Earl Irvin West. Unfortunately, it is out of print and sometimes difficult to find.

One of the earliest references to the church in the United States is found on a tombstone in Cane Ridge, Tennessee, dated to 1807. A preacher named Barton Stone had convinced a Presbyterian group there to leave their association and return to following only the teachings found in the New Testament. They wrote up a "Last Will and Testament" for their old church in 1804 and began calling themselves a church of Christ.

Yet, Cane Ridge is not the first group to do so. Dr. Robinson, principle of Overdale College in Birmingham, England, states, "In the Furness District of Lancashire, in North West England, there existed in 1669, during the reign of Charles II, a group of eight churches of Christ. Most of them are not now in existence. An old minute-book has been found on the year 1669 and it shows that they called themselves by the name church of Christ, practices baptism by immersion, celebrated the Lord's Supper each Lord's Day, and had elders and deacons. There was also a church of Christ in Dungannon, Ireland, in 1804 and in Allington, Dengigshire. In 1735, John Davis, a young preacher in the Fife District of Scotland was preaching New Testament Christianity, twenty-five years before Thomas Campbell (Alexander Campbell's father) was born."

The fact that confuses many people is that the churches of Christ have no central headquarters or defining body. Each congregation is independent and autonomous. What creates a church of Christ is not its association with an organization, but an adherence to an idea: that the Bible alone defines what is the church. As a result, churches of Christ are often self-starting as people read their Bibles and decide to return to the simple beginnings of the church. Thus groups spring up and fade away over time often without direct connection.

A fairly good description of the church can be found in Wikipedia under "Church of Christ." There is a discussion group devoted to recording finds past indications of these self-starting congregations. It is called "Traces of the Kingdom." Keith Sisman maintains a website on the topic which is also called "Traces of the Kingdom."