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I quickly tried this in my environment and got it working.

1. Create a single action list called "Chores"
2. Added 3 chores, each as a task
3. Set each of the tasks as "due again" after 1 day

When I complete one of the tasks, it disappears and re-appears the next day (you can simulate this by bringing down the view options -> CMD-SHIFT-V, and choosing availability filter: remaining).

For those tasks I did not check off, they appear in my list the next day but don't duplicate.

Your default filter for actions should be set to "available", not remaining. Save this as a perspective called "Chores" and go to it every day to see your chores you need to do.