Chitin is obtained by mining Abyssal barnacles found on Leviathans which appear as living, moving islands in the Ocean. A 'random' encounter, once located will return to the same position on the map... It appears as a very 'round' island with the large barnacles scattered about on the surface. After a short time 'harvesting' with a pickaxe, the 'island' will shudder and begin to submerge, beware on how long you spend mining the resource.

Good luck. I've come across 2 now and know where to return, ;).