this would be worked:

1. join the mages guild
2. bought the chameleon spell (any)
3. have the pass to arcane academy
4. have at least level 20 alteration skill
5. have at least 5 grand soul gem with grand soul inside
6. have any suit with no enchantment: 2 rings, amulet, pants, shirt
7. enchant each 5 of those item with chameleon spell with grand soul gem you have
8. every item will be have an enchantment of 20% chameleon and the stacked enchantment will be 100% chameleon that will makes you permanent invisibility even if you attacking

if you dont wanna go to arcane academy you can enchant via the console just type "showenchantment"

This trick worked in Morrowind but since you're talking about the Arcane University I'm guessing you mean Oblivion. So, moving this to Oblivion Spoilers...

Interesting you can still get 100% Chameleon though. I would have thought they'd put a stop to that.

Ascendent Sigil Stones can grant you 25% Chameleon. That means you can attain this effect through four items with no need to work your way into the University.