Double-yolkers, as chicken people call them, are actually a “mistake,” according to the helpful people at Poultryhelp.com. They’re what happens when a hen ovulates too quickly, or “when one yolk gets ‘lost’ and is joined by the next.” Inside the chicken. Sometimes it’s hereditary.
A year ago, in Juneau, I had the pleasure of looking at all the eggs a chicken has inside it at any one time. Before Karen Waldrip learned that the marten was living inside the chicken yard, the sneaky bugger got more than a few eggs and carried off at least one chicken. She found another maimed, with its scalp hanging down; she killed it to stop the pain. When she butchered it she found all the eggs inside that the chicken would have laid. There were about eight of them, and she saved them in a Ziploc in the freezer, in the order in which they would have been laid. The littlest was like the tip of my pinky, and the largest was a full-size yolk without a white on it. The albumen, membranes and shell are added at the last minute (Excellent brief primer on egg production.)
Double yolks hardly ever result in twin chicks, sadly, because they’re so likely to fight each other before they hatch.
Incidentally, eggs sometimes have other problems. Sometimes they come out without any shell. Or if they reverse direction inside the chicken’s egg-assembly line before they come out, they may get another layer of white and shell. Eggs without yolks used to be called “cock eggs,” because, Poultryhelp says, people thought roosters laid them. But now, so much more accurately, they are called “fart eggs.”