5th Singularity E Pluribus Unum: Des Moines (Surveillance Fortress) free quest is the best AP & time-saving location to farm Claw of Chaos. You'll get about 2x Claw of Chaos by spending 180AP.
7th Singularity Babylonia: Ur (Jaguar Park) free quest is one of the other locations to farm Claw of Chaos. You can also get Seed of Yggdrasil.
2nd Singularity Septem: Germania (The Dark Forest) is the first location you unlock to farm Claw of Chaos, but the item rarely drops.
You can also farm Claw of Chaos at Wednesday Daily Quest: Berserker Traning Ground. For other item drops, check the table below.
5 Star Servants Tier List
Best Craft Essence
Oda Nobunaga (Archer)
Best Servants [★4]
Zhuge Liang (Lord El-Melloi II, Waver)
Cu Chulainn (Lancer)
Piece of Year 2030 (A Fragment of 2030)
Talk on the Heated Sands
Victor from the Moon