The following things will break the chain
Using your rollerskates or bicycle
Encountering a different type of pokémon from the one that you started the chain with
Encountering a wild pokémon that was not in a shaking patch of grass
Leaving the area
Saving and restarting from where you left off
So,you will not break the chain if you save but if you restart your system,it will break.
Source: Guide to chaining.
Hope I helped!