You know the security
chains which allow a door
to be opened slightly, but can only be unlatched by closing the door and sliding the end of the chain
along a steel channel which widens at the end furthest from the jamb? Here's how to get through a door so equipped without cutting the chain:
Get a rubber band, or similarly elastic object, and a thumbtack. Open the door, perhaps by picking the lock. Reach inside the door, and attach the rubber band to the sliding end of the chain (probably using this technique). Stretch the band towards the centre of the door, and use the thumbtack to pin it to the door. Close the door. The rubber band will contract, pulling the chain across with it. You should now be able to knock the chain free by banging on your side of the door. (Depending on the door, it might be better to have the rubber band pulling the chain slightly upwards as well as across, so that it's lifted closer to the hole which allows it to be released.)
Disclaimer: I haven't tried this, but it sounds like it should work. I learnt the technique from a novel by Donald E. Westlake, which I think was either "Enough" or "Trust Me on This"--I'm at least sure it wasn't one of his Dortmunder novels. /msg me or email if you know the reference.