Earned by fusing a Chaos Crystal with at least 50 or so charges with a compatible ranged weapon such as a bow. The bow will be unidentified and always require 14 strength to successfully wield. Upon attacking enemies a few times, will reveal a random enchantment upon the weapon followed by repeatedly upgrading the weapon every few tiers (+1,+2 etc.) as well as further reducing the requirement to wield, which increases the efficiency.
It is recommended that if there is a specific enchantment desired, save the game and then monster hunt until the desired enchantment is reached. Also note that infusing any cursed ranged weapon will remove the curse and generate an entirely new weapon whilst consuming the old one, so no need to worry about cursed chaos weapons.
If the enemy dodges a thrown arrow, the Chaos Bow will burst chaos magic on you.