Does playing a unit start a chain?

Yes, playing a unit does start a chain.

According to Rule 332, whenever a card is played, a chain is created. However, units have a specific interaction with the chain that prevents opponents from reacting to the unit itself.

The Sequence for Playing a Unit:

1. Chain Creation: When you play a unit, it is placed on the chain.
2. Finalization: The unit goes through the "Finalize" step.
3. Immediate Resolution: Unlike spells, units skip the "Execute" and "Pass" steps. They resolve immediately upon being finalized.
4. No Priority: Because the unit skips the steps where players would normally receive priority to react, opponents cannot play reactions to the act of playing the unit itself.

Important Nuance: While you cannot react to the unit being played, if that unit has a "When you play me" triggered ability (a Play Effect), that ability does go on the chain as a pending item after the unit enters the board. Players can react to that triggered ability once it is on the chain.

Reference: Rule 332, Rule 333.1.c, Rule 376.4.a, and RiftJudge FAQ #8333.