Should I change my chain? It broke once, but its condition seems rather good
The tool to check for "chain stretch" is incredibly cheap -- something every halfway-serious cyclist should have. 

And chain breakage is most often caused by poorly executed shifting under load or a poorly adjusted derailer. (Though another cause is a poorly joined chain.)

(Poor lubrication is unlikely to cause the chain to break as a first indication -- excessive wear of chain and cogs is far more likely, and the chain will only break when wear has reached extreme levels.)