Chicken or the Egg?

I love when I get allusions without having to look them up, because, honestly, I won't look it up if I don't get it.

"'Gentlemen,' he said, and unwrapped a drumstick from a piece of newspaper. 'I reverse the order. For Bryan's sake. As a tribute to the Great Commoner. First the chicken, the egg'" (page 126).

This is an allusion to William Jennings Bryan, who was an American politician during this time and died in 1925. He was famous for many things, but in this particular case I think they are talking about the Scopes Trial. Bryan was a fundamentalist, so he didn't believe in evolution. John Scopes, on the other hand, was caught teaching evolution in schools. Bryan fought against Scopes and wanted him persecuted.
Bill and Jake are going to eat the chicken first, then the egg, because that's how Bryan would have wanted it.
I don't really know if this really pertains to the plot or theme. I'm really having a hard time making a connection. They are just having lunch, so the mood is very lighthearted. I mean, Bill is there and Robert is out of the picture, so of course the mood isn't serious. Also, I think they are a little drunk.


P.S. I had some help from my history notes from school last year.