You could fiddle a bit with the chunk sizes, to ensure that you would only read/dump files from and to disk every so often. If your maps are pretty simple, the amount of data in memory shouldn't be a problem. To my knowledge this is the same way Minecraft does it.
You could also cache a bigger amount of chunks, say two concentric circles worth around the one the player is currently in.
I can't see this becoming a problem on modern computers.
Try the sample that's for download on my Blog - I haven't experienced any problems, and the chunks there are very small, to illustrate the concept. If you make 255x255 chunks you would load a lot less and the files would still be fast to read and not too much of a strain on memory.
Kind regards - Jakob