On the mundane level, what the OP generator asked suggests by inclusion, an involvement betwixt the two components.
If at a deeper level, you are asking what came first. the chicken the egg or the chicken-egg conundrum? Then I would hazard that although there is debate about the first two, the conundrum must be last as the nonexistence of either of the other two negates there being an enigma to solve.
However, if your proposed problem is with the egg generating a chicken (or visa versa) and not some dissimilar or older more ancient oviparous organism, then I should imagine as most philosophical thinking is done over breakfast, the egg that sparked the issue has a higher than average chance of being that of Gallus gallus than other poultry or indeed that of any other bird, fish, monotreme, amphibian, lizard or dinosaur, and further more and notwithstanding, the chicken is but an exemplar for all the above and their inclusion in both the mystery and the conclusion to it, (if ever reached) is implicit.