Put simply, if we are referring specifically to a chicken egg, then of course the answer is the egg. Neil DeGrasse Tyson, the famous American Astrophysicist, wrote: “Which came first, the chicken or the egg? It was the egg – laid by a bird that was not a chicken.” This bird has been referred to as a “proto-chicken”, an intermediary between the present day chicken, and a preceding common ancestor. The same can be said of a Robin, a Blackbird or any other of our wonderful garden birds.
All birds in existence today evolved from a group of theropod dinosaurs which lived in the Mesozoic era, approximately 225 million years ago; Dinosaurs were reptiles, egg-laying creatures that were the first to evolve the ability to create an outer shell for protecting the egg from water, or other moist environments. Modern day birds have simply continued that reptilian tradition, with the added benefit of some design enhancements with regards to colour, shape and texture.
The egg, therefore, most certainly came before the chicken.