Hi, breaking the chain is certainly one way, but first check if the part of the derailleur that the chain passes through has a small screw at the rear end. Undoing this would enable you to separate the chain from the derailleur much more easily.
Check the chain to see if it uses a missing link ?
The link is a two piece one that you press tightly together at the pins then slide the two pieces together for disconnection. Grime/dirt can hide the appearance of a mssing link so you may have to give the chain a good wipe to see it.
As Nealh says, if you do need to remove the chain. look for something like this. One of the links should be different. But not always. If there is no "master link" then for very occasional use, you can get a cheapish chain link removal tool to remove it.