The story
Attested in variant form since 1393. The surface of some cheeses, particularly unaged ones, resembles the surface of chalk: white, crumbling, but in substance cheese is much softer than chalk. It is interesting to note that lime chalk and cottage cheese forms a glue-like material used in the restoration of ancient half-timbered houses, perhaps suggesting an alternative original meaning.
Etymology from Wiktionary, CC BY-SA 4.0.