In Arthur Clarke's Childhood's End, there is a small allusion to a Chesterton story when the characters Stormgreen and Van Ryberg discuss their theories about the nature of the Overlords (Chap. 4):
"I admit, " said van Ryberg, "that some of my theories haven't been very successful . But tell me what you think of this one. "
"Must I?" sighed Stormgren.
Pieter didn't seem to notice.
"It isn 't really my idea, " he said modestly . "I got it from a story of Chesterton’s. Suppose the Overlords are hiding the fact that they've got nothing to hide?"
"That sounds just a little complicated to me, " said Stormgren, beginning to take slight interest .
'What I mean is this, " van Ryberg continued eagerly . "I think that physically they're human beings like us. They realize that we'll tolerate being ruled by creatures we imagine to be- well, alien and super-intelligent. But the human race being what it is, it just won 't be bossed around by creatures of the same species . "
"Very ingenious, like all your theories, " said Stormgren. "I wish you'd give them opus numbers so that I could keep up with them. The objections to this one... [they're interrupted when another character arrives in the scene] "
Searching in google for
chesterton history mentioned in "childhood's end", I did not found an answer. The only thing I found is this list of allusions from Shmoop, where Chesterton is shown, but not the specific story.
So, which Chesterton story is alluded in Childhood's End? Do Arthur Clarke said which story is that, or is it possible to someone more versed in Chesterton works to discover that?