A general Rule
Food can be categorized into two:
1. Food which does not contain meat, fat and their extracts
It is not necessary for the Muslim to question the person who prepared the food about his beliefs or disbelief, or whether or not he had touched the food, even if that inquiry is very convenient and natural for one who wants to ask. In short, all kinds of food with the exception of meat, fat, and their extracts are permissible for a Muslim, even if he doubts that it might contain something which is forbidden for him to eat or doubts that its cook —whosoever he may be— had touched it with wetness.
https://www.sistani.org/english/book/46/2044 /
2. Food which contains meat, fat and their extracts
It is necessary for the Muslim to get Yaqeen (certainty) about the meat and its extracts that it is a Halal meat (ritually slaughtered according to Islamic Law).
From the above rule there are three exemptions i.e. even if we do not have Yaqeen (certainty) of Halal meat but Islam considers it Halal:
1.
Yadul Muslim: (یَدُ المُسْلِم) If someone purchases meat from a Muslim, it will be considered Halal (ritually slaughtered according to Islamic Law) until he gets Yaqeen that the animal was not slaughtered Islamically.
2.
Souq ul Muslimeen: (سُوقُ المُسلِمِینَ) If someone purchases meat from a Muslim Market then the meat will be considered Halal even if he doesn’t know about the religion of a seller.
3.
Manufactured in an Islamic Country (الصنع في بلاد الاسلام)
https://www.sistani.org/arabic/qa/02044/ [Question 3]
In all the above three exemptions there is no need to do further Inquiry.
Now coming back to your question, if you are eating meat or chicken from a Muslim Restaurant then there is no need to inquire but if you are eating from a Non-Muslim restaurant then you should get certainty (Yaqeen) that it was slaughtered Islamically. It doesn't matter how you attain this Yaqeen; from the words of a chef, manager, your own research or any other way.