New Scientist has a feature on the back page called The Last Word, in which readers submit puzzling questions for other readers to answer. One of the questions posed in the most recent issue of New Scientist we received was titled Twin Chicks, and has to do with the photo below:

"Upon cracking open my breakfast boiled egg," the reader wrote, "I found a whole new egg inside (see photo). This is not a double-yolked egg, it is a double-egged egg — a completely new egg with a shell and yolk inside another."
"Can anyone explain it?"
Well, the reader made several mistakes here. First of all, he asked this question in the March 24-30 issue of New Scientist, meaning that it would be answered (well, neglecting publication lag) in the issue spanning April 1. Second, he neglected to specify that the question be answered truthfully.
Naturally, I took this and ran with it....
Forthwith, my response to New Scientist:
There's a perfectly simple explanation for this double egg. This isn't exactly a case of twin chicks; one is, in fact, an intruder. This is a seldom-seen example of the fiendishly cunning reproductive strategy of the Lesser Retrochronic Cuckoo, cuculus asimovii.
The better-known families of cuckoo, as everyone knows, lay their eggs in the nest of a foster-parent, leaving the foster, or host, to incubate their eggs for them. Occasionally, though, a host may detect the cuckoo's egg and throw it out of the nest. The retrochronic cuckoos have a unique mechanism for circumventing this defense: Their eggshells contain high levels of thiotimoline, a complex organic molecule possessing strong endochronic properties.¹ This enables cuculus asimovii to insert its eggs into the clutch of the host before the host's eggs have even been laid. The host then re-lays the cuckoo's egg along with its own clutch, and having actually laid the egg itself, is extremely unlikely to suspect the egg's actual provenance until it hatches.
Since thiotimoline is quite volatile, it very rapidly sublimes out of the eggshell once the eggs are exposed to the atmosphere. Within a few minutes after laying, the shell is almost entirely devoid of thiotimoline and no longer possesses any significant endochronic properties, leaving the egg apparently perfectly normal. As a result, there is only a very narrow window of possible detection after laying.
There are, naturally, certain risks inherent in this process. The retrochronic cuckoo's goal is to place its own egg among those waiting to be laid, but an egg whose shell contains unusually high levels of thiotimoline may be inadvertently inserted too early in the egg-forming process, and in such cases it is possible the cuckoo's egg may actually be incorporated within one of the eggs of its host, as in the example you have discovered. When this occurs, it is in most cases fatal to both offspring.
[1] The Endochronic Properties of Resublimated Thiotimoline, I. Asimov, Ph.D (biochemistry), 1948
This response was, of course, prominently datelined April 1, 2007.