Winegar is great for removing chalk stains, the water here is hard too and I use winegar all the time. Fill a bowl with it and perhaps half water, put all your dishes in for an hour - you can reuse the winegar. While you're at it, unscrew the thingy's on the taps in your kitchen and bathroom sink and put them in too.

Oh, and if you have an electric kettle, fill that half up with winegar too - it will be as good as new.