An egg, as we know it today, is the membrane-bound container inside which an embryo (unborn offspring) can grow and develop. Eggs first developed around 340 million years ago, however the egg that we know it (characteristics such as asymmetrical shape and a hardened shell,) first evolved around 150 million years ago. Through the process of evolution, different forms of egg began to develop resulting in the development of the egg we see today. These eggs having further functions that can result in an embryo having the environment it needs to develop i.e. a chick having the environment (such as the ability to respire and store nutrients) it needs to eventually hatch and develop into a chicken.

The first chicken to have existed would have been a result of a mutation produced by two animals that share very close properties to that of a chicken. When they mated, a genetic mutation occurred resulting in the combining of DNA to create the chicken. However, the first chickens evolved around 58 thousand years ago. Therefore, compared to that of the egg, the chicken evolved much later than the egg resulting in the egg coming before the chicken.

Resources:
https://www.science.org.au/curious/earth-environment/which-came-first-chicken-or-egg

https://www.smithsonianmag.com/smart-news/problem-solved-the-egg-came-first-6910803/

https://www.treehugger.com/finally-answered-which-came-first-the-chicken-or-the-egg-4864321#:~:text=So%20in%20a%20nutshell%20(or,then%20it%20hatched%20a%20chicken.

This question irks me, and I avoid engaging in debate around it because there really is no black and white answer. As you suggest, in order for there to be a chicken, there must be egg (of some description), however for there to be a chicken egg, there must be a ‘chicken’. So for this I remain mixed.

Another possibility for a mixed opinion is that maybe the chicken and the egg occurred concurrently, in which case it would be hard to choose one answer.

If there is no egg, there would not be any chicken. Perhaps the egg comes from another species or something, and it hatched into a chicken. When there were no chickens, two birds that were almost-but-not-quite chickens mated and laid an egg that hatched into the first chicken. This is an evidence that eggs come before chickens.
Also, some may say that without the chicken's warmth, the egg will not be able to hatch. However, another bird, can also sit on the egg to provide the warmth, just as the mother duck sat on the swan egg in The Ugly Duckling. There may not be a consensus, but I think all evidence points to egg before chicken.

Link: https://www.sciencefocus.com/nature/which-came-first-the-chicken-or-the-egg/#:~:text=Eggs%20are%20much%20older%20than%20chickens.&text=But%20it%20doesn't%20matter,then%20the%20egg%20came%20first.

Most people agree that chickens evolved from some other bird, so I think it depends on how you define the egg...

Some other bird (Bird x) lays an egg with a chicken inside. Is the egg a chicken egg because it contains a chicken, or is it still a bird x egg because it came from bird x?

Eggs definitely came before chickens but I'd imagine this question is more specifically about the chicken egg

The “chicken” came first, the egg and all that is the egg had to come from somewhere, whether it was an evolutionary ancestor or it’s parent. The egg can’t exist out of nowhere, the male and female have to provide the dna, proteins etc to create the eggs and lay it so that that animal can lay another egg.

Other animals that evolved before chickens laid eggs too. Dinosaurs laid eggs with shells like chickens. Before them animals laid eggs with thin membranes in water. On a literal level eggs definitely came before chickens.
(jeez how long does it expect this response to be? looks like it requires 300 characters but some things are more simple than that)

The debate over whether the egg or the chicken came first has been addressed by both scientific and philosophical perspectives. Scientific evidence supports the idea that the egg came before the chicken.

For:

Evolutionary Biology: From an evolutionary standpoint, the egg predates the chicken. Birds, including chickens, evolved from reptiles, which were laying eggs long before birds appeared. The first chicken would have come from an egg laid by a bird that was not quite a chicken but had evolved sufficiently to be classified as the first chicken.

Genetic Mutation: The process of genetic mutation occurs during reproduction. A bird that was not quite a chicken (a proto-chicken) would have laid an egg containing a genetic mutation that resulted in the first true chicken. This means that the egg containing the first chicken existed before the first chicken hatched.

Against:

Circular Reasoning: Some may argue that for an egg to be considered a "chicken egg," it must be laid by a chicken. However, this perspective often results in circular reasoning, as it requires defining when a non-chicken bird becomes a chicken.

In this magic world, there is various way to make such animal. And in my theory of today, to answer to the question, I would say it depend on the race of chicken or the country.