empower opens a chain?

Yes — activating an Empower ability opens a chain. Empower is an activated ability keyword (Rule 827.1), and all activated abilities use the chain (Rule 377.3): the ability goes on as a pending item, the game enters a Closed State, and your opponent gets a chance to play Reactions before it resolves (FAQ #12333).

A couple of nuances:

• Since Empower has no speed tag, you can only activate it on your own turn, during a Main Phase, with no chain or showdown in progress.
• You can only start the next Empower once the first chain has fully resolved. Also note the Empower ability itself doesn't target its source (Rule 827.1.b.1), so "can't be chosen" effects like Deflect don't stop it — but your opponent can still react with removal or disempower effects while it's on the chain.