Chaos weapons are special because they are Fire damage weapons that have additional damage that scales with Humanity (up to a maximum of 10 humanity)So chaos weapons will always be better (assuming identical stats) to Fire.
To create a Chaos Weapon you need to begin with a standard weapon ( one that you can appply pine resin to otherwise it is unique and will not work )
Then you will need to locate Chaos Flame Ember which is found in the Demon Ruins ( See vid for the location and credit to MichelKobayashi for the vid) and give this to Vamos who is located in the Catacombs,This allows Vamos to Upgrade your +5 Fire weapon to Chaos and Chaos +5. Vamos automatically is able to make Weapons of Fire to +5.
In order to complete the Chaos weapon from scratch you will ultimately require 9 Titanite shards , 9 Large Green Titanite shards , 8 Chunks of Red Titanite and 1 Red Titanite Slab
Red Titanite Chunks - Lost Izalith the tentacle monster plants can drop them and they respawn apparently, However the best place to farm chunks of all kinds is in the Kiln of the First Flame at the end of the game...The Black knights there are respawnable and 100% chunk drop rate.
Red Titanite Slab - Rare drop from Chaos Eater in Lost Izalith
and in a treasure chest prior to boss area.
Here is a Chart which was created by an unknown so credit to whoever they are.
TRICK-To get the achievement without using your items simply fully upgrade the item in one shot and wait until the achievement pops WITHOUT leaving the upgrade window thus not allowing the game to save the data then simply turn off the game and turn back on. Supposedly worked on Demons Souls