h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The question is insoluble because it is based on a false premise. There was no first chicken and no first chicken egg. No matter how far you go back in time along the line of chicken ancestors, the difference between any two generations will be the same as it today between a mother chicken and her daughter. There is no place where you can draw a line and say: 'this is a chicken and it's mother is only a proto-chicken'. You might just as well declare that you are a separate species from your parents because you look a bit different from them.

You've got to calll it a proto-chicken at some point. Eventually you'll even hit the dinosaur stage... and an egg had to come before whatever you designate as the proto-chicken. It's not clearly defined, but it is still inevitable.

So the question should be: What came first, the dinosaur or the egg?

Of course not!
All philosophical questions involve either cats or chickens, not dinosaurs. Scrodingers cat, and the question why the chicken crossed the road are examples. Dinosaurs just don't factor in...

The question doesn't specify a chicken egg, merely an egg.