Does equipping a gear go on the chain?

Yes, equipping a gear card uses the chain.

According to RiftJudge FAQ #10734 and Rule 818.1, Equip is an activated ability. When you activate an equip ability, it is placed on the chain, which provides players an opportunity to respond with [REACTION] cards before it resolves.

The Sequence for Equipping:

1. Activation: You pay the equip cost and target a unit you control.
2. Chain Starts: The equip ability is placed on the chain as a pending item.
3. Priority/Reaction: The game state becomes Closed. Players (starting with your opponent) may now play [REACTION] cards in response to the activation.
4. Resolution: If the chain resolves and the target remains legal, the gear attaches to the chosen unit.

Important Nuance: As noted in RiftJudge FAQ #634, if an opponent plays a reaction that removes the target unit from the board before the equip ability resolves, the equip ability will fail to resolve because its target is no longer legal.