[Working with a Merchant Who Sells Imported Chicken]

The answer—and Allah is the granter of success—is that the permissibility of the slaughter of the People of the Book is a matter of scholarly disagreement: some scholars deemed it lawful while others deemed it unlawful.
If this worker is buying and selling with a man who deems it lawful, and the people of that land deem it lawful, then the buying and selling are permissible and its price is lawful for the owner of the business; assisting him in what is lawful for him is permissible. What is not permissible is assisting him in what is unlawful to him. This is what appears to me, and Allah knows best.
If it be said: If the matter is as you described, then it would be permissible for a Muslim to hire himself out with a dhimmī to sell wine, engage in usury, sell pork, and the like.
We say: It is not the same. What we have mentioned is a matter of valid disagreement among Muslim scholars, they said, “every mujtahid is correct”—and thus the permissibility of eating the chicken mentioned in the question and buying and selling it is a recognized position in Islam; whereas selling wine and the like is something forbidden in the religion of the Muslims, and there is no doubt about that among them collectively.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2