It's worried me all my life.
I mean, if you want two different things then cha-chas and cheese, or chaff and cheese, or church and cheese would make so much more sense.
Chalk and cheese...well, if you take Wensleydale cheese, for instance:
then it's much the same colour as chalk, it's crumbly like chalk, and can be cut into the same sort of shapes...
...and I bet that if someone made it into paint and charged enough for it then plenty of idiots would decorate their houses with it, too.
Word To Use Today: cheese. This word comes from the Old English cēse, from the Latin cǣseus. Amusingly, it's related to the Old Saxon kāsi.
Apparently chalk and cheese has been worrying people at least since John Gower's Confessio Amantis in 1390. The only explanation people can come up with is that it does sound quite snappy.
*By the way, my children's version of Don Quixote is out today. I suppose I could do a link about Don Quixote and Sancho Panza themselves being chalk and cheese; but that's a bit obvious, so I'll just point out that the delicious cheese Manchego comes from La Mancha in Spain, just like DQ and Sancho.