The chicken definitely came first.
Before the egg, before the incredible egg.
Production of an egg by any bird, chicken or otherwise, is an impressive feat.
Each species of bird produces a unique egg. Size, color, shape, number — all differ. What is constant is the process of production, the mechanics.
The egg is like a space capsule, a self-contained world for the developing chick. All the nourishment and water it needs to grow is there when the egg is laid. The egg breathes, good air in, bad air out. There is accommodation for waste.
The yolk holds all of the fat and most of the protein the chick needs. (That's why you might be relegated to Egg Beaters.)
Precocial chicks — like geese or killdeer — are up and running within hours of hatching. They hatch from eggs with larger yolks. Altricial chicks — like songbirds — are born helpless, eyes shut, no feathers. Since much development is done after hatching, those species can afford eggs with smaller yolks.
Energy not spent producing larger yolks then is spent feeding nestlings. (Precocial chicks can feed themselves.)