Does First Mate's "When you play me, ready another unit" open up a chain to be reacted to?

Yes, First Mate's "When you play me" ability creates a chain that can be reacted to.

According to the rules and FAQs regarding "When you play me" triggered abilities:

1. Playing the Unit: When you play First Mate, the unit itself enters the battlefield immediately and does not use the chain (it cannot be reacted to).
2. Triggered Ability: The "When you play me" ability triggers immediately upon the unit entering play. This ability is added to the chain as a pending item.
3. Reaction Window: Because the ability is now on the chain, the game state becomes "Closed." This creates a window where players can play Reaction cards in response to the ability before it resolves.

Sequence:

1. You play First Mate.
2. First Mate enters the battlefield.
3. The "When you play me" ability is added to the chain.
4. Players receive priority to play Reaction cards.
5. Once all players pass, the ability resolves, and you must ready another unit (if a valid target exists, it must be chosen, even if it is an enemy unit).