The problem with the time period that Chadwick is writing about here is that the main source that we rely upon is Eusebius, and many people are somewhat concerned about his objectively in relation to the church prior to it becoming the official religion of the Roman Empire. It is not that we do not have many primary sources, we have quite a lot, but most of them deal with how one should conduct themselves as a Christian, or how a church should operate. Eusebius, outside of the New Testament, is really the first person who sat down to write a history of the church.
Eusebius was a Roman bishop who pretty much came to fame after Constantine 'converted' to Christianity, though the reasons behind his conversion are dubious at best. Some suggest that the reason he waited until his dying breath to become baptised was because of the belief that one could lose salvation if one was baptised too early. However the other idea (and one that I tend to hold) was that Constantine's conversion was more of a political decision rather than a personal spiritual decision. As the story goes, he had a dream before a major battle where he was told that he would conquer by the Cross, so he had all of his men paint a cross on their shields and go into battle.
Actually, Constantine didn't go into battle, he ended up letting the battle come to him, so as it turned out, his victory was not some spiritual intervention (like some in the Bible) but a rather clever strategy. Basically the armies were standing on the opposite ends of a bridge, and Constantine remained where he was while his enemy (a rival claimant to the imperial throne) crossed the bridge and was slaughtered.
The reason for making Christianity the state religion was, once again, not some spiritual decision but rather a pragmatic one. Rome had been struggling with multiple claimants to the throne for decades and now Constantine had risen to become the sole emperor. One of the best ways to stamp your rule onto an empire is through the use of religion. The traditional Roman religions were eclectic at best, with no one particular god holding sway. Basically people worshipped how they say best. What Christianity offered was consistency, namely one God and one set of rules to follow. Therefore, the idea was to get rid of the multitude of gods and personal morality to replace it with a single God with a single set of rules.
Eusebius formed part of the council of Nicea, which was the council set up after Constantine decreed that Christianity would be the sole religion of the empire, and worked to lay out a strict, consistent, foundation. This included bringing the Bible together as a consistent book. The Bible that we have now was basically determined by vote from this particular council. Mind you, I do not have a problem with the content of our modern Bible, or with its teachings, however I do have a problem with people's interpretation of its teachings.
This is an interesting, second source account of the early church, and I also suspect that Chadwick uses more sources than just Eusebius in writing this. I wouldn't necessarily refer people to Eusebius though, because he tends to waffle on a lot using a lot of theological writing. He is typical of what one would expect from a Christian author writing a Christian history, and no doubt writing something that is revisionist as well.