Chicken and eggs are complements in production. If the price of chicken goes down, what happens to the supply curve of eggs?thanks

In this answer, I am assuming that you are talking about
the price that can be gotten by selling the chicken, not
the price of producing the
chicken.

If the price for which chicken can be sold goes
down, the supply curve for eggs will shift to the left.  In other words, the supply of
eggs will go down, assuming that chickens and eggs are complements in
production.

The reason for this is simple.  If the price of
chickens goes down, farmers will raise fewer chickens, all other things being equal.  If
farmers raise fewer chickens, there will also be fewer eggs laid.  When that happens,
the supply decreases and the supply curve moves to the left.