According to evolutionary biology, hard-shelled amniotic eggs evolved about 312 million years ago. This allowed ancient reptiles, fish, and dinosaurs to lay eggs on land long before birds ever existed. In contrast, the modern chicken (Gallus gallus domesticus) was only domesticated from the red junglefowl roughly 3,500 to 8,000 years ago.
But, the scientific argument for the chicken coming first relies on a specific protein called OC-17. This protein is strictly required to accelerate the formation of the chicken's eggshell, and it is produced exclusively in the ovaries of a hen. Under this logic, you cannot have a true chicken-laid egg without a chicken to produce the shell.
Ya see, it goes back to ancestors of chickens, perhaps back to the single-cell varmints that crawled out of the sea.
This triptych explains it all.
'
The Garden of Earthly Delights' by Heironymus Bosch,
ca. 1490-1510, Museo Nacional del Prado
(tap on image for ultra hi-res version)
Note evolution depicted in left panel. His IQ probably 165
+. Da Vinci ~ 180. The estimated IQ of Blaise Pascal is between 180 and 195.