What you see: White, stringy blobs on the yolk when you crack open an egg
What it is: The chalazae, essentially a set of strands built into the egg to anchor the yolk in the center
Eat or toss: Eat! This is simply part of the egg
First things first. Is there any chance—any chance at all—that that white goopy strings in the egg is, um, something a rooster left behind*? Or, erm an embryo? Or, maybe an umbilical cord?
Good news: No to all of the above. Such things range from impossible to extremely unlikely as the standard eggs we buy at the store are not fertilized. So, what’s up with those weird white strings draped over the yolk?
Those strings are called the chalazae. Their job is to keep the yolk suspended in the clear part of the egg, which is called the albumen. When the yolk is formed inside the chicken’s body, the yolk spins inside the albumen; during this process twists of protein fibers, the chalazae, form on the top and bottom of the egg. Think of them like little harnesses that cinch the yolk to keep it from moving around too much. (Check out The Virtual Chicken, an excellent video produced by Auburn University, for a grand tour of egg making inside the chicken.)
You might even count seeing the chalazea as a good thing. The more visible it is, the fresher your egg is.
And now, loyal readers, it's time for an egg-stra credit question. What are those dark spots on the yolk pictured below? Check out this EatOrToss post for the answer.
*For real! Some people jump to this conclusion. Proof.
Pat Curtis - Head of Prestage Department of Poultry Science - North Carolina State University
Anatomy of an Egg - Exploratorium
What are the White Things That Hang Off an Egg Yolk?
What's That Weird, White String Inside a Raw Egg? Behold, The Chalaza
Chalazae - Eggcyclopedia - IncredibleEgg.org
What's The difference between fertilized and unfertilized eggs? Chowhound
Don't yolk with me! I'm the chalazae!