It is part of the egg white and can be cooked and eaten along with the rest of the egg.
It does not make the egg unsafe.
It does not mean the egg is fertilized.
And it does not indicate the presence of a parasite.
Some cooks remove it when preparing recipes where they want an especially smooth or uniform texture, but that is mostly a matter of preference.
For an ordinary breakfast, you can simply cook the egg normally.
Other Things Inside Eggs That Can Look Strange
The chalaza isn’t the only natural feature of an egg that can surprise people.
Occasionally, you may crack an egg and notice something different from what you’re used to seeing.
Blood or Meat Spots
Small reddish or brown spots can occasionally appear inside an egg.
These may form during the egg’s development and are not the same thing as an embryo.