...........assuming you're talking about amniote eggs - those with protective shells and embryonic membranes (like the amniotic sack)?
I'll assume you are since the implication and popular assumption is that the question refers to the chicken egg.
Anyhow, Galliformes (the taxonomic group that chickens belong to) can be traced right back to some putative examples from the Late Cretaceous - some 100 - 65 million years ago.
Amniotic eggs howver, can be traced to approximately 340 million years ago.
So the unequivocal answer would be that the humble egg predates the chicken by quite some margin.