Green’s Dictionary of Slang

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

1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 189: ‘To walk the chalk’ ? a military manœuvre to discover which is drunkest.
1825		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.
1828		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.
1848		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’.
1856		Life in Boston & N.Y. (Boston, MA) 23 Aug. n.p.: [He] is often in such a fix that he can’t walk a crack.
1876		Edinburgh Eve. News 1 Dec. 4/4: Now, chalk a mark along the floor. If I’m drunk I can’t walk it.
1884		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.
1901		Portsmouth Eve. News 27 Sept. 4/1: I’ve learned it doesn’t do to talk [...] / An’ so I simply walk the chalk.
1902		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.
1913		Sport (Adelaide) 5 Apr. 10/2: They Say [...] That He could walk a chalk line, I don’t think.
1922		‘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.
1933		‘William Juniper’ True Drunkard’s Delight 225: He [...] cannot spot a right line, can’t walk a chalk.
1952		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.