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Casualty N means “As an additional cost to cast this spell, you may sacrifice a creature with power N or greater.” and “When you cast this spell, if a casualty cost was paid for it, copy it. If the spell has any targets, you may choose new targets for the copy.”

If there's only one card in your library as A Little Chat resolves, you'll put it into your hand.

If you pay the casualty cost of a spell, the copy will resolve before the original spell.

The copy of the spell is created on the stack, so it's not “cast.” Abilities that trigger when a player casts a spell won't trigger.

You may sacrifice only one creature to pay a spell's casualty cost, and you copy the spell only once.