Most scientists believe that birds developed from reptiles. Since most reptiles to this day reproduce by laying eggs, it's rational to assume that the first bird-like creature came from an egg, too. (Genetic material remains constant throughout life, so the first creature that evolved into what we would consider to be a bird must have originally existed as an embryo inside an egg.) It would then have laid eggs and - over millions of years, perhaps - birds as we know them slowly developed and produced different species. The present-day chicken is one of these, but - 'way back when - its great-great-grand-daddy almost certainly came from an egg.
The egg pre-dated the bird, if you believe in evolution. Of course, fundamentalist believers in the Bible will say that God created all the creatures as creatures. In that case, the bird pre-dated the egg. Take your pick!