When a chicken is butchered for meat, the egg sacks sometimes contain partially formed eggs. The shell hasn't formed yet, and the egg white hasn't been made, but they do have the membrane that keeps the egg together. They are mainly yolk, but the flavour is less sulfurous than a regular yolk. You've probably eaten these only in processed food, but you can sometimes get them from butchers who specialize in chicken.
When boiling them, the membrane keeps the egg together. They can be eaten cooked like this or peeled to leave just the yolk. I should also point out that these eggs are unfertilized, hens don't need to be fertilized to lay eggs.
You can see half a chicken in this photo below with a egg. Behind you can see bags of eggs and chicken ovaries. A fairly typical Thai market scene.