I have thought about that one alot, and it is definitely the chicken.
Heads up, evolution forced lifeforms in to such complexed beings that it was necessary for them to share DNA in order to create sturdy offspring.
The whole progress is quite shady, but it must have been that some pre-poular-organism has made the first egg ever, from which the first of the now know chicken was born. To put it simpler, lifeforms were able to reproduce by just shedding of cells, this has evolved in to a more sophisticate progress, so the egg was 'created' first, and then the trick off laying those was passed on to the next of kin...