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
gaming.stackexchange.com/users/71634/Soltara of the first flam
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
gaming.stackexchange.com/users/71021/Thorst
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.
gaming.stackexchange.com/users/71635/user71635
In Brightstone Cove Tseldora, you can farm the peasant farmers for titanite shards/chunks.
Better drop rate than dark wraiths in DS1 too, haha
gaming.stackexchange.com/users/71711/guest8888
Use the bonfire ascetic in cardinal tower,in the room with 4 big crossbow pointing at you,below is a chest that will contain 3 titanite chunk,if you wish to repeat you must defeat the giant and the pursuer again..
gaming.stackexchange.com/users/71753/Muchhhjjjj
I don't know about early game, but if you beat the game, you can buy infinite from stone trader Chloanne.
gaming.stackexchange.com/users/157885/Peaceful8
Where can you farm Titanite Chunks in Dark Souls II?   Titanite Chunks can ascend +7 weapons to +9. There do not seem to be any chunks accessible early in the game, where can I farm this item?
Where can I farm Titanite Chunks?
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gaming.stackexchange.com/questions/159792
gaming.stackexchange.com/users/45820/Mondrianaire
It's a little late in the game, but the  Black Gulch  is a good area to farm titanite chunks and large titanite pieces. You can also try the dwarves in Gyrm's Respite and farm the peasant farmers in Brightstone Cove Tseldora. Some locations, such as Brightstone Cover Tseldora, offer drops like titanite chunks.
The community suggests few locations.