[patsylimerick]

Apparently scientists have (sorry ) 'cracked' it.

Growing a good egg: Metadynamics simulations show that the eggshell protein ovocleidin-17 induces the formation of calcite crystals from amorphous calcium carbonate nanoparticles. Multiple spontaneous crystallization and amorphization events were simulated; these simulations suggest a catalytic cycle that explains the role of ovocleidin-17 in the first stages of eggshell formation.

Now, the protein ovocleidin-17 is found within the bird's ovaries and therefore, there cannot be an egg without there first being a bird. So the chicken (or something like it) evolved and then established this protein which allowed it to produce eggs.

qed