punctuation - How many hyphens in University of Oxford-based?

If I attach "-based" to a compound noun, should I put a hyphen between every word? As in:

I worked for a University of Oxford-based company

Or:

I worked for a University-of-Oxford-based company

Granted, there are probably better ways of phrasing this. I'm just curious what the prescriptive usage on hyphens would be in this situation.