A double-yolked egg is familiar. An egg within another egg?! That's a rarer phenomenon—but real, nevertheless.
According to Countryside Daily, it's called "counter-peristalsis contraction" and occurs when a second oocyte (the ovum that becomes the egg yolk) is released by the ovary before the first egg has finished its journey through the oviduct and been laid.
The first egg (which is, at this point, in the eggshell gland where, as the name suggests, the shell is deposited over the egg) reverses course and is pushed back towards the top of the oviduct and typically added to the just-released oocyte (that is, the second, most-recently released future yolk). The two then travel together down the oviduct and the shell is deposited over both.
Typically, this results in an very large egg with normal-sized yolk and white plus an entire fully-formed egg inside. (Even more rarely, tiny fully-formed eggs are found within regular-sized eggs.)
So what they say in Countryside Daily article is true: "When raising chickens for eggs, expect the unexpected."
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