Bicycles/Maintenance and Repair/Chains/Removing a Bicycle Chain
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Removing a bike chain usually requires a chain tool which can be purchased for a small amount.
Many older bikes, without a derailleur, have a master link that can be opened with a flat-head screwdriver.
Modern SRAM chains also have a master link that functions in a totally different way. It can be opened by pushing the plates of the masterlink parallel to each other. This can be done with your hands, or if it's gummed up it may require pliers. These links are compatible with Shimano chains, as long as they are for the same number of gears on the cassette. i.e. 7, 8 or 9 cogs.
On older chains the best way is to use a chain tool, place the chain in the tool and carefully line up the tool's pin with a rivet of the chain and tighten until the pin pushes the chain pin far enough out that it's only inserted through one outer plate of the chain. If the rivet is pushed all the way out, it won't be possible to reinsert it. Pull the chain apart.
To put back together, reverse the process. If the newly joined link is tight, use the second position of the chain tool to loosen the link. Be sure the rivet is centered on the chain.
On modern Shimano chains you should push the original rivet out entirely and replace it with a special replacement rivet, reinstalling the original pin is likely to cause the chain to brake at that point.
Anytime a chain without a master link is cut it is weakened. It is preferable not to cut a chain if possible. For example when installing a derailleur, it's better to disassemble and reassemble the derailleur than to cut the chain.