I beat him by long chalks. Thoroughly. In allusion to the ancient custom of making merit marks with chalk, before lead pencils were so common.
Walk your chalks. Get you gone. Lodgings wanted for the royal retinue used to be taken arbitrarily by the marshal and sergeant-chamberlain, the inhabitants were sent to the right about, and the houses selected were notified by a chalk mark. When Mary de Medicis, in 1638, came to England, Sieur de Labat was employed to mark “all sorts of houses commodious for her retinue in Colchester.” The same custom is referred to in the Life and Acts of Sir William Wallace, in Edinburgh. The phrase is “Walk, you're chalked,” corrupted into Walk your chalks.
In Scotland, at one time, the landlord gave the tenant notice to quit by chalking the door.
“The prisoner has cut his stick, and walked his chalk, and is off to London.” —C. Kingsley.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894