The answer is not directly, though one of his most powerful sentences is a thumbnail sketch of the idea:
That is the paradox of the whole position; that henceforth the highest thing can only work from below.And, for completeness, here is the correlate in his fiction:
[GKC, The Everlasting Man CW2:313. Also cf. Jn 13:2-15]
...you remember that he [Peter] was crucified upside down. I've often fancied his humility was rewarded by seeing in death the beautiful vision of his boyhood. He also saw the landscape as it really is: with the stars like flowers, and the clouds like hills, and all men hanging on the mercy of God.But of course Chesterton never used the term "Subsidiarity", since it only entered the vocabulary of Catholic Social Teaching in the early 1960s in John XXIII's Mater et Magistra and Pacem in Terris, but as you ought to expect, GKC has various hints and comments which grow out of his consideration of Rerum Novarum (1891), which perhaps someday some scholar will investigate.
[GKC The Poet and the Lunatics 21-22]
But when I looked into this matter, I found (as usual) a very funny little bit which I think you will enjoy:
[Regarding the manner of M. Anatole France in dealing with Joan of Arc:] Because her miracle is incredible to his somewhat old-fashioned materialism, he does not therefore dismiss it and her to fairyland with Jack and the Beanstalk. He tries to invent a real story, for which he can find no real evidence. He produces a scientific explanation which is quite destitute of any scientific proof. It is as if I (being entirely ignorant of botany and chemistry) said that the beanstalk grew to the sky because nitrogen and argon got into the subsidiary ducts of the corolla.Now, GKC was trying to be funny - and he was. You may not know what argon is - it's an inert gas. Or what a corolla is - that's the term for the petals of a flower. But you've surely heard the word "subsidiary" recently - or at least something very close to it.
[GKC ILN Mar 28 1908 CW28:72]
Now, when I first glanced at that lovely little jargon, I had to laugh. There's so much like that these days - people trotting out science words without any real awareness of their meaning. Sometimes it's very funny. For example, I recently heard a term "unobtainium" and laughed, since there really is an element called "dysprosium" which means almost the same thing in Greek! Actually the Greek root means "hard to get at", since it is one of the rare earths and was particularly hard to get at. And of course the inert gases like argon are also hard to get at - there's a great story about the discovery of argon but I probably ought not go into that sort of topic here - or at least not today. [Welll... if you want to find out, see Jaki's The Relevance of Physics 255. The discussion actually ties into the larger one we've been having about "error" since it reveals some deeper truths about the nature of such things as "error" and "precision", to say nothing of more human issues like honesty. Fascinating - maybe next week!]
But this idea of elements which are hard to get at, coupled with that botany word "corolla" - which I first read as "corona" - well, that made me think of that very strange element called "coronium".... No it's not on the Periodic Table. It was found in the corona of the sun, but of course it was eventually found on earth wearing a disguise.
There's another hard-to-find element called "nebulium" - it gives a strange lurid kind of green to certain odd things far out in space. But like "coronium", it was eventually found to be something found here on earth, but in a kind of disguise.
Now, the funny thing about all this is that the "coronium" and "nebulium" are the ones which are wearing disguises, or (to be quite accurate) have had their earthly clothes partially removed - and so they reveal themselves in a very unusual light.
Alas, I am not expressing myself well today - I am quite busy just now, and perhaps leaving out what I should include, and including what I should leave out. Perhaps I should just leave you with this somewhat longer fragment of our Uncle Gilbert, which perhaps will unite my thoughts for me, as he so often does:
...there is something mysterious and perhaps more than mortal about the power and call of imagination. I do not think this early experience has been quite rightly understood, even by those modern writers who have written the most charming and fanciful studies of childhood; and I am not so presumptuous as to think that I can scientifically succeed where I think they have somehow vaguely failed. But I have often fancied that it might be worth while to set down a few notes or queries about this difficult and distant impression. For one thing, the ordinary phrases used about childish fancies often strike me as missing the mark, and being in some subtle way, quite misleading. For instance, there is the very popular phrase, "Make-believe." This seems to imply that the mind makes itself believe something; or else that it first makes something and then forces itself to believe in it, or to believe something about it. I do not think there is even this slight crack of falsity in the crystal clearness and directness of the child's vision of a fairy-palace - or a fairy-policeman. In one sense the child believes much less, and in another much more than that. I do not think the child is deceived; or that he attempts for a moment to deceive himself. I think he instantly asserts his direct and divine right to enjoy beauty; that he steps straight into his own lawful kingdom of imagination, without any quibbles or questions such as arise afterwards out of false moralities and philosophies, touching the nature of falsehood and truth. In other words, I believe that the child has inside his head a pretty correct and complete definition of the whole nature and function of art; with the one addition that he is quite incapable of saying, even to himself, a single word on the subject. Would that many other professors of aesthetics were under a similar limitation. Anyhow, he does not say to himself, "This is a real street, in which mother could go shopping." He does not say to himself, "This is an exact realistic copy of a real street, to be admired for its technical correctness." Neither does he say, "This is an unreal street, and I am drugging and deceiving my powerful mind with something that is a mere illusion." Neither does he say, "This is only a story, and nurse says it is very naughty to tell stories." If he says anything, he only says what was said by those men who saw the white blaze of the Transfiguration, "It is well for us to be here."Yes, that's the word I left out, the hidden theme of those hard-to-get-at elements which revealed their unearthly reality by a new light - "Transfiguration".
[GKC The Common Man 56-7 quoting Mt 17:4]
P.S. I had forgotten this particular, very Tolkien-esque, bit about Story - it is utterly splendid. Now,perhaps, you will understand a little about why I like to write about Quayment...