My take was that the chicken in the question was simply understood with the royal meaning, as in, the first animal to lay eggs.
From there, I know that there would have to be a pre-egg laying chicken, or pchicken somewhere in this timeline.
At some point, the pchicken would produce offspring, wherein one of the trillions upon trillions of instances when a new combination of genes produces a new trait in an organism, this instance happens to be one where an organism encases its offspring in an encasement.
So to me, the pchicken exists, and then the egg with the new organism - the royal chicken - exists, from which hatches the first chicken.
Thanks for bringing up the question - I'd never actually looked at it from a christer propagandist's view. : )