Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
What is predominant about way the Christians nowadays slaughter is by electric shock if they are sheep and goats, and they do nearly the same thing with chicken, and they shoot cows in the head. Please refer to fatwa:82323
These ways of slaughtering are not Islamic, and it is not permissible to eat the meat of animals slaughtered in this way as they are dead meat. Allah says (interpretation of meaning): Forbidden to you (for food) are: Al-Maytatah (the dead animals - cattle-beast not slaughtered), blood, the flesh of swine, and the meat of that which has been slaughtered as a sacrifice for others than Allah, or has been slaughtered for idols, etc., or on which Allah's Name has not been mentioned while slaughtering, and that which has been killed by strangling, or by a violent blow, or by a headlong fall, or by the goring of horns - and that which has been (partly) eaten by a wild animal - unless you are able to slaughter it (before its death) and that which is sacrificed (slaughtered) on AnNusub (stone altars). (Al-Ma'idah 5:3)
However, you can eat the chicken of the Turkish man if he is a Muslim and if it is slaughtered by him, or if he informed you that it was slaughtered according to Shariah, provided he is a trustworthy person.
We have previously published detailed Fatawa regarding the ruling of the animals slaughtered by the people of the book, one of which we referred to above. Please refer also Fatwa: 81456.
Allah knows best.