You can upgrade Chaotic and normal items at the item upgrade shop. Upgraded Chaotic items require you to be at least level 700 in order to use them. Every time you upgrade it, it increases the items power by 40%. Items can be upgraded until +5. For example, say you had an item that did 100 damage. If you upgraded it to +2, it would do 140 damage, and at +5 it would do 300 damage.
NOTE: Rare and Legendary items can be upgraded as a normal item. They have their own upgrade forms that are more expensive.