Sort of, anarchy does not mean individualism. It absolutely can be built around syndicalism and federation. If a group of people says, "we believe it's best to take turns doing this labor" then they can do that.

Typically there's a cultural expectation of "wellbeing for all", which becomes a significant social expectation. If it's the cultural standard, it changes the relationship to chores significantly - I can contribute to them knowing that the general person out there is also doing chores with my wellbeing in mind.