The Chromatic Sword is an ilvl 45 Uncommon (green) sword that is extremely rare because of it's unique looks. This two-hander has a chromatic particle effect that is not seen on any other weapon in the game, and since it's Bind on Equip, it's one of the most valuable items in the entire game!
The sword drops from a rare spawn called Scale Belly. This mob spawns with intervals between 1 and 3 hours in the Crystalvein Mine in the northern part of The Cape of Stranglethorn.
Because of the insane value of the sword (usually several million gold), expect Scale Belly's room to be full of other players as well as bots, so farming his is very difficult. You can tag him if someone else from your own faction tags him first, but he will die very fast since he is only level 60.
Even if you manage to kill him, the chance of getting the Chromatic Sword is very low. No one knows for sure about the drop rate of the sword, but it's believed to be around 2 - 4 %.
The best strategy is to group up for a 5-man group and camp him. Everyone in the group will get to loot him, so it essentially gives you 5 chances instead of only 1. However, don't farm him in a raid group, or else only one person will get to loot him!
There is no other source for the sword, so camping Scale Belly is your only bet. Good luck with hitting the jackpot!