A  chicken is defined as a fully matured bird of the subspecies gallus
  gallus domesticus.

  A chicken egg is defined as an egg which  will  eventually  hatch  and
  will  result  in  a  bird that will grow up to be a chicken as defined
  above.

  It then follows that the last pre-chicken bird or proto-chicken on one
  sunny  day laid an egg with a mutation that caused this egg to produce
  a chicken rather than a proto-chicken.

  Hence, the egg came first.

  So there's that.

  But wait, that's just one egg! Where do all the  other  chickens  come
  from?

  The mystery continues.