Green’s Dictionary of Slang

walk the chalk v.

also walk a/the crack, …a chalk, walk chalk, walk the chalk line

to walk along a chalked line in order to prove one’s sobriety.

[UK]‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 189: ‘To walk the chalk’ ― a military manœuvre to discover which is drunkest.
[US]J.K. Paulding John Bull in America 118: I had qualified myself by being able to walk a crack after swallowing half a gallon of whiskey.
[US]R.M. Bird City Looking Glass V ii: I don’t stagger, and I can walk the crack with any man, only I’m giddy, – that’s all.
[UK]Exeter & Plymouth Gaz. 19 Aug. 6/1: What my short epitaph would be, (if I should walk my official chalk) — ‘Too little work and too much talk’.
:
[UK]Edinburgh Eve. News 1 Dec. 4/4: Now, chalk a mark along the floor. If I’m drunk I can’t walk it.
[UK]N. Wales Chron. 26 July 4/6: The landlord of a hotel in the streets ona Suynday not able to ‘walk a chalk’ is certainly a deplorable novelty.
[UK]Portsmouth Eve. News 27 Sept. 4/1: I’ve learned it doesn’t do to talk [...] / An’ so I simply walk the chalk.
[UK]Lichfield Mercury 5 Sept. 3/4: The police [...] turned a deaf ear to his request [...] to be allowed to write his name, or walk a chalk line, as evidence of his sobriety.
[US] ‘Gooseberry Wine’ in T.W. Talley Negro Folk Rhymes 41: Don’t never tu’n yo’ back, Suh, / On day good ole gooseberry wine! / Oh walk chalk, Ginger Blue! Git over double trouble.
[UK]‘William Juniper’ True Drunkard’s Delight 225: He [...] cannot spot a right line, can’t walk a chalk.
[US]J. Jones From Here to Eternity (1998) 728: He says he’s never seen a man yet, crazy or not, that he couldnt make walk the chalkline if they give him a free hand.