Certainly there are many examples of embryonic stages of animals that develop outside the body of the parent, and are protected from the elements by some kind of membrane or shell, and thus we define them as eggs. Many of the simpler forms of eggs are the normal mode of development of the lower vertebrates and invertebrates, and most certainly the earliest forms would have predated the eggs of chickens, birds and reptiles by hundreds of millions of years. However, since I am discussing the eggs of chickens, which are birds that descended from reptilian ancestors, here I will consider only eggs of this lineage.
In this case I define an egg as the kind with which we are most familiar, the kind with a hard shell. Fossil evidence indicates the first eggs with hard, heavily mineralized shells first appeared in several reptile groups as early as the Lower Triassic, around 220 million years ago. Many membranous and poorly mineralized eggs probably existed among reptiles as early as 310 million years ago, but little is known about them because they didn't fossilize well . The first avian ancestors appeared around 150-200 million years ago. Because early birds and egg-laying dinosaurs coexisted, it is difficult to determine the origin of fossilized eggs of this era unless the embryos are exposed or the parent is found with them. However, since birds evolved from Therapod dinosaurs that are known to have had mineralized eggs, it is reasonable to assume that the early birds also had mineralized eggs [2,3]. There are few known examples of eggs from the earliest days of avian evolution which can be positively identified as belonging to a bird. The earliest known example of a fossil bird egg is an unhatched bird in its egg found in China in 2004 and estimated to be 121 million years old .
On the other hand, evidence suggests the domestication of the chicken began around 10,000 years ago in the southeast Asian peninsula, and it was likely descended from both the Red and the Gray Junglefowl native to the area. From there the chicken spread westward and reached Egypt by about 1500 BC. Interestingly, there is no mention of fowl in the Old Testament .This would indicate a much later origin for the chicken, certainly much later than that of the earliest known bird egg.
Based on this information it is clear that the hard shelled avian egg with which we are familiar predates the chicken by more than a hundred million years, and therefore the egg came first.