Where can I farm Titanite Chunks?

Solution 1:

It's a little late in the game, but the Black Gulch is a good area to farm titanite chunks and large titanite pieces. The best part is, there is close to zero risk of you dying from this, once you get the hang of it.

Shoot the black tar pits with a fire arrow, and the creatures will die from fire. When they are dead, run up, collect items, and repeat. Use a bonfire Ascetic at the first bonfire, to get the mobs to respawn. You can shoot at the tar pits a little after the first bonfire. If you use a bonfire Ascetic at the second bonfire, the boss will respawn, but not the mobs.

To farm the second area, stand at the exit of the second bonfire, and you can ignite the 5-6 tar pits quickly and easily. Best part is, when you replay it in NG + later games, this will not make the area significantly harder, because you can use the same cheesy tactic, to take out the mobs, without danger to yourself.

This will also net you quite a lot of souls. Remember to equip the Jester's cap: http://darksouls2.wikidot.com/jester-s-cap + Covetous Gold Serpent Ring: http://darksouls2.wikidot.com/covetous-gold-serpent-ring

Solution 2:

Join the Princess Bell Covenant, and wear the ring the little guy gives you. Beat the invaders and you will get a chunk every time you succeed.

It was the first covenant I joined. It was really fun and I now have 50 chucks because of it

Solution 3:

I'm not sure the drop rate, but if you don't want to join a covenant, I managed to get a chunk off one of the dwarfs in Gyrm's Respite.

If i remember correctly it was the Shield Type.

Solution 4:

In Brightstone Cove Tseldora, you can farm the peasant farmers for titanite shards/chunks. Better drop rate than dark wraiths in DS1 too, haha