Which came first: The Chicken or the Egg?
Most theories about origin of life say that unicellular organisms were first and multicellularity (like chicken) evolved much later, so in that meaning egg (single cell)* was first. Also, almost all chicken ancestors lay eggs (primitive birds, non-avian reptiles, amphibians, fishes and so on...) so eggs existed much earlier than chickens.

*in the meaning of zygote. The development of chicken embryo starts in hen's oviducts, so it's not a single cell at the moment when hen lays it (Gilbert, 2000).