I have a relative who remain in a non-Muslim country where only a few Muslims exist. He is afraid of eating chicken and beef as he does not know who and how the animal slaughtered. What does Islam says about this? Is it permissible to take the food when I can't ensure Islamic slaughtering rule for animal as most of the people are non-Muslims there?
Well as we know Surat al-Maida is one of the last revealed (revealed after the treaty of Hudaibiah) Surat of the Quran!
And in verse 5 you can read the following:
"All the good and pure things have today been made lawful for you; the food of the people of the Book is lawful for you, and your food for them, Likewise you are permitted to marry chaste believing women or chaste women from among the people who were given the Scripture before you provided that you give them their dowries and become their protectors in wedlock; this permission is not for sensual license or secret illicit relations; whoever rejects the way of Faith, all the deeds of his life shall become vain and he shall be a bankrupt in the Hereafter" (see also the translation of sahih international here)
This means that according to some conditions (pork and alcohol free and methods of slaughtering the animals) you can eat food non-Muslims eat, for example, when you have been invited by them with the restriction of anything which is not halal (like pork and alcohol for ahl-al-Kitab), but it wouldn't be halal to eat meat from non-Muslims who are not among the people of the book.
So if you find a Muslim Grocery or Halal Food (in Many countries super markets provide halal chicken) it is of course the best to take this kind of food and you should avoid any other.
But if you have no other possibility to get beef or chicken and you want/need to eat them, according to some Scholars (a few years ago I thought this is the opinion of only a few scholars like ibn 'Arafa al-Maliki -who was quoted in a book of al-Qaradawi- and the scholars of al-Azhar, but it seems that this opinion has a larger basis) you could eat this as the Verse does allow it and to be "safe" some of them suggest to say bismillah and allahu akbar before eating this non slaughtered beaf/chicken.
And don't forget Islam is a religion of easiness ( الإسلام دين يسر) not a faith of uneasiness!
Other related posts:
Are there special cases in which meat not slaughtered in Islamic way is allowed to eat?
Is it permissible for a Muslim to eat something which is offered by a non-Muslim?
stunning animals before slaughter - different opinions
It is considered as a haram meat if you eat meat in non-Muslim countries. (Totally, from the viewpoint of Shiite school of thought). Unless it be clear that the (Muslim) Zabiha or slaughterer (Zabiha) slaughtered by saying بسم الله الرحمن الرحیم namely "Bismillah-e-Rahman-e-Rahim" (and by its Islamic canonical conditions). Of course, seemingly, dear Sunni brothers believe that being Ahlul-Ketab would be considered as a condition to allow…
On the other hand, as a helpful opinion:
Usually, there are many Islamic shops in many non-Islamic countries, such as Turkish, Pakistani, Arab, Iranian, and other Islamic shops, that you can provide your food from there (if you trust them as halal…).
Tl;DR: The default state of food for People of the Book is halal. But for meat, we do have more specific requirements, so we check them. Allah says in the Qur'an that mentioning His Name is a requirement, and from Sunnah we learn that the time of this is always during slaughter.
Animals killed by non-Muslims do not have the name "Allah" pronounced even if all other rules of Islamic butchery are satisfied. As a result of this, if a Muslim, knowing that it's slaughtered by a non-Muslim, eats meat, he'll be considered as having stealed the right to life of an animal (similar to stealing rights of other people) in the hereafter and this'll cause him increased torment of the grave. See this for my full answer: https://islam.stackexchange.com/a/76023