I've read that 1 in 1,000 eggs has double yolks, so it is likely that you could encounter this even with a small backyard flock of chickens.  To go back to the car wash analogy in my previous post, a double yolk egg can occur one of two ways:

1.     More than one "grape" (ovum) drops into the oviduct at once.  This often happens with young pullets, whose reproductive system is still working on getting properly synchronized.  It can also be hereditary in some cases - a few people have reported that their hens (usually heavy breeds) always lay double yolk eggs.

In the car wash analogy, this is as if two cars went through bumper-to-bumper, rather than individually with plenty of space between them.

2.    Ovum #1 gets hung up in the line, until ovum #2 comes along and knocks it loose.  The two ova then travel down the rest of the oviduct together.  Imagine one car gets hung up in the car wash, and the next car bumps into it.  They then move through the rest of the car wash in lock step.

A double yolk egg is usually considerably larger than a normal egg.  Large enough that some of the pictures I found made me wince for that poor hen!  The PoultryHelp.com website has a page cataloging some of the many strange ways that an egg can go wrong, including "fart eggs" (eggs without a yolk) and the fascinating "egg within an egg" phenomenon. 

Most of these egg oddities are laid by young hens, or just represent a statistical quirk.  If your hen chronically lays odd eggs, it could indicate a nutritional or genetic problem.  The occasional weird egg is nothing to worry about, but should be celebrated!  With lots of pictures, please!