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.
Rashoumon event (Ibaraki Douji event)
Murder at the Kogetsukan
Inheritance of Glory
5 Star Servants Tier List: Best Servants [5/9 updated!]
FGO Reroll Tier List [5/11 updated!]
Best Servants [★4]: 4 Star Tier List
4th Singularity: London
Fate Grand Order Farming Items
Tamamo no Mae
Archer Inferno (Tomoe Gozen)
Kato Danzo (Katou Danzou)
Jeanne d’Arc (Alter)
Trick or Treatment
We'll Conquer the Ocean of Stars
Castle of Snow