It can't be done in Oblivion. Not without mods (i.e. cheating).
First, chameleon is not very effective in Oblivion unless it is 100%. It makes it progressively easier to sneak around with chameleon, but the player isn't invisible until 100%. And the higher the chameleon the more costly the spell.
I forget what the max chameleon effect can be enchanted with a grand soul gem. It is something like 8%. You'd need to wear 13 items with 8% chameleon to get to 100%. Player can't wear 13 items! In Morrowind we could. Morrowind would let us wear shirt and pants, then a robe, then 10 pieces of armor, and then two rings and one amulet!
In Oblivion you can only have a shirt/pants/shoes, OR a robe/shoes, OR armor. And there are only 4 (I think???) pieces to a full set of armor. Plus two rings and amulet.
It is much smarter to use plain old invisibility spell. Bind it to a hot key. Use it when you get in a pinch. If you interact with the world the invisibility wears off, so use the hot key to re-inviso yourself. A 60 second invisibility isn't very costly at all. Just remember to reapply it after using doors and opening containers, and talking to NPCs.