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The Chicken came from an Egg
This is a circular reasoning. To have a logical answer we have to determined a time frame for it, for example in a certain time period. If in that time frame, the chicken is observed first, and at the end of the time frame, no eggs is observed then the question is FLAWED!
Eggs were a form of breeding a long time before chickens. So a better way to phrase this question is "What came first the chicken or the chicken egg" if that is what the question intendeds to convey.
Something which wasn't a chicken laid an egg, and because of mutation, the result became a bit closer to a real chicken. This continued for thousands of years until a real chicken of today emerged from the egg. So, the real chicken of today emerged from the egg of a "not-really" chicken.
From an evolutionary standpoint, mutations have to be passed on through offspring. Thus, the ancestor to the chicken had offspring that were one step closer to becoming the chicken. Note that the ancestor itself did not become closer to being a chicken.
Only God knows, because he created everything living.
To lay an Egg there has to be a Chicken