Despite the fifty-cent wording, this question boils down to the age-old question "Which came first, the chicken or the egg?". The dilemma arises once one realizes that both answers could be construed as correct, depending on how the question's parameters are defined. Did an egg born of non-chicken parents develop into the first chicken, or did a chicken produce the first chicken egg as a matter of reproduction? These questions and dozens more like them lead researchers down the path of causality. Did an egg cause the appearance of chickens, or did chickens cause the appearance of chicken eggs?
One camp holds that the egg must have come first. There were direct ancestors of the modern chicken which did indeed produce eggs. While most of those eggs produced genetic copies of the ancestral bird species, a few eggs may have contained enough genetic mutations to create the first modern chicken, albeit from two non-chicken parents. Therefore, the first modern chicken must have been hatched from a egg which no longer contained the genetic coding to reproduce the ancestral bird species.
Another camp suggests that the chicken came first. Through the concept of creationism, one could argue that God created all species of animals, including the modern chicken. There was no genetic mutation necessary; chickens reproduce themselves through the fertilization of egg cells, which would naturally mean the chicken arrived first on the planet and the egg is always going to be one generation behind.
There are plenty of counter-arguments and semantic questions surrounding the chicken or the egg causality dilemma. Some argue that the word "egg" is not limited to chickens in this construction, thus giving the advantage to the egg, because many ancient species of animals reproduced themselves through eggs long before the chicken evolved.
Others argue that the chicken must have arrived before the egg because there would have been no hen to nurture the first egg if it came first. The egg is considered an offspring of the chicken, not the other way around. Without genetic mutation, only chickens could produce chicken eggs, so they must have arrived first.
The "chicken or the egg" dilemma can also be seen as a question of semantics. In the question itself, the chicken is mentioned before the egg, so one could argue for the chicken's earlier arrival. Some people also answer the question by saying the word "chicken" comes before the word "egg" in the dictionary, so once again the chicken wins the bet.
Recent studies have strongly suggested that the "chicken or the egg" dilemma scientifically favors the egg. There were direct ancestors of the modern chicken called jungle fowl which could have produced slight mutations over time that resulted in the birth of the first chicken. Some adherents to a mix of evolution and the intelligent design theory suggest that God may have created the evolutionary path which would eventually result in the first birth of a modern chicken from an ancestral egg.