Rear cassette 'ticking' forward, making chain catch, what is the problem and how do I solve it? I have a Giant Rapid 4, bought in 2009.

When freewheeling (i.e. rolling forward but not pedalling) on my bicycle, the chain catches. I had a look and I think this is because the rear cassette sometimes gets 'caught' slightly and moves with the wheel. 

This doesn't seem to be a problem when pedalling, but when I am not pedalling and the front gears are not moving, the chain catches. It actually broke my chain. 

Just put a new chain on, but I'm reluctant to ride it until this problem is resolved fully, otherwise the new chain will be stressed and may break again.

So, what could cause the rear cassette to be 'carried' forward by the wheel? Is it a bearings problem, or do I need a new cassette? Thanks.

Edit. I took off the cassette and dismantled the hub, it was the freehub body which was broken. It sounded and felt like one of the bearings inside it was broken. However the Shimano freehub disassembly tool is no longer sold and I couldn't find one second hand. The rim was worn anyway so I treated myself to new wheels and reused the old cassette, which was still ok.
Most likely the free hub is sticking.  The grease can get old and sticky.  Service the hub.  Lots of videos on youtube. Or take the hub to a shop.  And you can wear out a hub - some parts are serviceable.  

Sticky hub is not likely to break a chain but it is a problem that needs to be corrected.