Eggs were used for millions of years before chickens evolved.
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Garda say: A non-chicken, but closely related, animal conceived an embryo that had all the proper mutations to create an egg that would carry to term and become a chicken. That's descent with modification.
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JosephV say: We do not say egg came first, since it is part of a lifecycle in many creatures.
First there was nothing. God said let there be light. Then material Earth, Sun and stars, then fish, trees, and so on. God created Adam, the first man. He then created them male and female. The egg is just a stage in the lifecycle of hens and poultry. God created all animals and He created them male and female. He gave us a chance to see and learn about our own selves.
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CRR say: God created the chicken which then laid the first egg.
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ce_fowler say: So where did the very first chicken come from then?
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Lighting the Way to Reality say: If the egg comes from a chicken, how could the egg be first?
The answer to the question of which came first, the chicken or the egg, is quite easy to understand from an evolutionary standpoint.
All animals produce eggs, including humans (female that is). So your question isn't applicable to just chickens.
The production of eggs as a means of reproduction was around a lot longer than chickens were. The first eggs were produced by early, simple animals several hundred million years ago. As the simple animals evolved into more complex forms over time, the production of eggs continued to be a part of the process of reproduction.
There are a great many fossils of small dinosaurs with feather impressions showing a wide variety of forms. The feathers would initially have been used for insulation, for there is evidence that the dinosaurs were at least meso-thermal instead of being cold blooded.
Subsequently, some lines of small feathered dinosaurs evolved into gliders and then flyers.