"Who does the chain belong to?"
Translation:Vem tillhör kedjan?
There's a big debate over whom that I don't want us to get into here. Suffice it to say that English language experts disagree among themselves (see e.g. http://www.macmillandictionaryblog.com/keeping-it-real-with-real-grammar) and that to who is common even in writing if you look at corpora. So let's just agree to disagree about that.
'Whose chain is it?' would be Vems kedja är det? in Swedish. That's probably a more useful sentence than the one we've got here, but still, we're trying to teach you the word tillhör and a grammatical structure where it's possible to use it.
I'm just wondering whether it's correct to split the verb and say Vem hör kedjan till? At least in German it's not unusual to split compound verbs that consist of another verb and a preposition. For example if the verb is zusammensetzen (to assemble, put together) you can say Ich setze es zusammen (I'm putting it together). Does it work similarly in Swedish?
Vem hör kedjan till is more like 'to who is the chain connected'. In practice the difference in meaning might be small, but it exists. Because of this, we use this word order more often in other combinations.
It's possible colloquially to say as you did 'Kedjan tillhör vem'?, it's like saying 'The chain belongs to who?' in English. You need to use a special intonation for this kind of question. But the most idiomatic way of creating a question in Swedish is to put the question word first: Vem tillhör kedjan?
You are however right that Vem tillhör kedjan? can also mean 'Who belongs to the chain?'