Can you react to a unit being played?

No, you cannot react to a unit being played.

According to RiftJudge FAQ #2971 and Rule 359.3, playing a unit does open a chain, but it resolves immediately and no player gains priority, which means there is no reaction window for the act of playing the unit itself.

Here is the breakdown of how this works:

1. Playing the Unit: When a player plays a unit, it is placed on the chain as a pending item.
2. Immediate Resolution: The unit resolves immediately as soon as it finalizes and enters the battlefield.
3. No Priority: Because units do not linger on the chain, players never receive an opportunity to play a [Reaction] card or activate an ability in response to the unit being played.

Important Nuance regarding "When you play me" triggers: While you cannot react to the unit being played, if that unit has a "When you play me" triggered ability, that ability will go on the chain after the unit has already entered the battlefield. Once that triggered ability is on the chain, you can react to it.