I know you have been looking for the answer for so long. You are not alone my friend. Even Aristotle was puzzled by the causality dilemma. He thought both the egg and the chicken must have always existed.
Let me just give you the answer first. It is the egg that came first, not the chicken. Here is the argument. In this reasoning, an egg is defined as the chicken egg if it has a chicken in it. A chicken like female creature mated with a chicken like male and laid an egg. Due to a small genetic mutation in the egg, the first chicken was born from that egg. So the egg came first.
AsapScience made a great video on it. Enjoy..
Source:
1. AsapSCIENCE, YouTube
2. The Guardian