Chalk and cheese means two things that could not be more unalike. They are chalk and cheese, as different as chalk and cheese, chalk and cheese those two.
It is British and is used almost always of two people compared. The pairing works because a white unaged cheese really does look like chalk while being nothing like it, and the phrase is attested from 1393.
1phrasechalk and cheeseTwo things that could not be more unalike.
“The twins are like chalk and cheese: one is shy and the other never stops talking.”
chalk and cheese is a contrast.
Attested from 1393, from the likeness in appearance between chalk and a white unaged cheese.
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. <!--Here is the earliest known use; it is technically Middle English, but it may be useful to somehow integrate it into the etymology.
Etymology from Wiktionary, CC BY-SA
Practised in Idioms