Which came first....

That takes a big assumption that the fall happened within a day of mankinds creation.
Why would you think that?

And your still left with the idea that God actually designed these creatures keeping in mind that they'd be drinking blood within a couple of days at most.

He actually designed them so they would die out if Adam and Eve hadn't sinned.

-KFC

 

The answers are quite straightforward, depending on your persuasion, evolutionist or creationist.

The strictly creationist - chicken first. Then it laid an egg, etc etc.

The evolutionist - egg first. It was laid, of course, by an almost chicken ancestor.

There would have been a long period as the chicken was coming into full chickenhood that it would be difficult to say whether it had finally reached full chickenhood or not . . . kind of like trying to pin down the time when a teenager becomes an adult.

About the absurdity of men just sort of happening to come along with the tubing, framework, etc etc etc: I certainly agree, that would be absurd.

Of course, that is not the theory of evolution, either.