Translation:He is studying chemistry at the university.
I wish I knew :). "På" works as well. If you are talking about a special institution of the uni, you will probably always use "på":
Han studerar på institutionen för kemi och kemiteknik.
Hm, I would probably say vid institutionen.
Then again, it doesn't really matter.
Maybe it differs between regions or just between different people. I definitely say "på KTH" and "på Chalmers", but maybe "vid Lunds universitet".
Both work, but vid is more literary and used with universities and institutions. På is more common in spoken language.
I searched in Korp, and "på Chalmers" is used more than twice as many times as "vid Chalmers". On the other hand, "vid Chalmers Tekniska Högskola" is a bit more common than "på Chalmers Tekniska Högskola", which makes sense with what you say since "Chalmers Tekniska Högskola" is more formal than "Chalmers".
I usually use på regardless of the university in speech and vid if it is written.
"He is studying chemistry at university" was marked as incorrect. So would the correct translation more so refer to a specific university. Eg; "Han studerar kemi vid stockholms universitetet"?