Masterlink Removal Tool/Chain Breaker
No tool kit should be without a chain breaker for Shimano chain pins or master link pliers for everything else (SRAM PowerLink/PowerLock, Wipperman Connex links, KMC Missing Link connectors, etc.). Don’t rely on the chain breaker that came with your little multi-tool. It’s worth shelling out $25, or so, for the real deal.
If you’re swapping out a chain, you may also want to consider changing your cassette. You’ll want a chain whip for this job, and bonus points if the handle pulls double duty as a pedal wrench.