The domestic chicken (Gallus domesticus) was bred from wild ancestors (mainly Gallus bankiva). Evolution (whether in the wild or through selective breeding) is a gradual process, but at some point there was a "first chicken" of the domesticated species, which hatched from an egg laid by a hen of the wild species. The egg came first.

It's the chicken or the egg, not the hen. And it really depends on your belief system. If you take the dogma literally then you can't in good faith ask this question. Now If you have an open mind and arn't so pragmatic I have an answer. Science has shown that a new species (eg. the chicken) comes first. In order to form an egg you need two chickens. This alone doesn't prove the statement though. Every original organism on the planet that comes into existence does not come into being the same way they're offspring do. An organism evolves based on need it adapts to it's enviornment FIRST then it finds a way to procreate. The chicken would then have to come first. The first directive of any organism is to survive, the second and sometimes more imparitive (as in the case of a mother protecting her children) is to perpetuate the species.
Long story short a chicken doesn't need to make babies in order for
it's self alone to survive. So a chicken would have to come first and then evolve a way to procreate to ensure species survival. This just happens at the same time a new species is created. Look at an amoeba, first a cell comming into being, then that same cell procreating by dividing itself into two. First the chicken, then the egg. Without the chicken there could never be an egg since the egg is a product of the chicken.

Chickens don't grow into eggs, eggs grow into chickens.

LOL bud that article was the one I was talking about, they say it seems to be life by mimicking DNA and RNA but hasn't been able to self replicate. Thats weird that you linked it to me, cool stuff either way though.

The egg was definitely around before the hen. Since chickens are a descendant of dinosaurs, and dinosaurs had eggs long before they had evolved into birds, the egg came first.