That's like asking if Eve's first son came before her! Of course the 'mother' comes first
Not exactly. It's more like the question of whether or not Adam & Eve had bellybuttons.
If you believe in creationism, then (I think) the general consensus is that God created the chicken first, which later laid eggs (just as in your example of Eve being created before she gave birth to any of her children).
But then again, you have to remember that in science it's extremely unpopular (and often career destroying) to believe in creationism.
So you have to look at the question of the chicken or the egg from the perspective of an evolutionist to appreciate the mystery behind it. And maybe we've been asking ourselves that same stupid question so long that we've forgotten why it was asked in the first place. Maybe that's the hundred bazillion dollar question, the answer to which determines which is more accurate: creationism or evolution.
Because otherwise, who really cares?
EDIT: Just read through some of the comments at the bottom of the follow-up article and see that (naturally) I'm not the first to come up with the possibility that the question is "Creationism vs. Evolution" in nature.