We can get an idea from his essay On Certain Modern Writers originally published in Heretics and recently republished in the excellent collection In Defense of Sanity. Chesterton discusses Christianity, the family and community in this essay, and makes the point that small communities like the family force different types of people to know and get along with each other. Ironically, it is the small community that is truly more broad than the large one:
In a large community we can choose our companions. In a small community our companions are chosen for us. Thus in all extensive and highly civilized societies groups come into existence founded upon what is called sympathy; and shut out the real world more sharply than the gates of a monastery. There is nothing really narrow about the clan; the thing which is really narrow is the clique. The men of the clan live together because they all wear the same tartan or are all descended from the same sacred cow; but in their souls, by the divine luck of things, there will always be more colors than in any tartan. But the men of the clique live together because they have the same kind of soul, and their narrowness is a narrowness of spiritual coherence and contentment, like that which exists in hell.That last sentence contains a typical Chesterton surprise. We might tend to think of "spiritual coherence and contentment" as something good, or at least not positively bad; and Chesterton plays on that conceit, leading us along in the sentence until shocking us at the end with his view that it is actually hellacious. What is hell like? It is a place where everyone has the same kind of soul, and far from being a place of discord and conflict, in fact there is "coherence" and "contentment." It is place where everyone is content in his sins. It is not a happy place, however, and so we can conclude that Chesterton sees a distinction between contentment and happiness. I am picturing Chesterton's hell as one of drabness and dullness, where everyone is "content" with his situation only because he doesn't have the energy to do anything about it. All the souls are the same because they are all worn down to the nub. Heaven, then, must be a place of glorious diversity (in the real sense, not the PC sense, of that word) where the souls are very different, and express the energy of their difference yet in the unity of God.
Back to the theme of this post, it seems clear Chesterton would have some problems with the Internet - the chief being that it is an ideal clique-forming ground, beyond anything Chesterton might have imagined. Now one doesn't need to be in physical proximity to spend all his time with the like-minded. A few clicks of the mouse and you can find somewhere online where everyone thinks exactly like you do. The everyday encounters that bring us into contact with a variety of people - like shopping, taking the bus, going to the library - may also be minimized via online shopping. "Sociability, like all good things, is full of discomforts, dangers, and renunciations" Chesterton tells us. On the internet, as soon as you experience any discomfort or any degree of renunciation, there is always another more comfortable page to repair to.
There is no neighbor on the Internet in any real sense, and thus no place for the second great commandment. "We make our friends; we make our enemies; but God makes our next-door neighbour." God commands us to love the man who is given to us in our circumstances; but what if our circumstances (e.g. online existence) are such that no one is given to us?
We have, in Chesterton's words, "a society for the prevention of Christian knowledge."
Of course I can't leave off here without discussing the irony of making this point on the Internet itself. The Internet itself is neither good nor evil - Chesterton would certainly agree with that - it is our use of it that makes it turn for good or ill. And so it is when internet "communities" begin to displace real communities that we begin to have a problem, and especially when people begin to think of online "communities" as real communities.