The thing you really want to avoid is the rat making a nest in your compost, and having lots of little rats. They like compost because it's warm, and can provide food. To discourage them from nesting, you need to stir your compost with a fork regularly - rats don't like having their home demolished. It may not be something to do when Mrs Fnaar is about though, as you might find lots of rats jumping out of the bin.
However, I'm quite surprised it got through your chicken wire defences - does the compost bin have a hatch? If so, is that covered with the wire? I've heard them referred to as rat doors - they're too small to get compost out through, but good for letting rats in.