Green’s Dictionary of Slang

1. (also lump of chalk) to talk.

1935		A.J. Pollock Und. Speaks 12/1: Bowl of chalk, talk.
1944		(ref. to 1855) Maurer & Baker in AS XIX:3 191/1: Bowl of chalk. Talk.
1946		St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI: 1 46: bowl of chalk. Talk. (Origin uncertain, but probably American.) Agreed. My men used lump of chalk, though Duke of York was commoner still.
1960, 1975		Wentworth & Flexner DAS 648/1–2: bowl of chalk – talk. [Ibid.] lump of chalk – talk.

2. to walk.

2001

M. Coles Bible in Cockney 23: They carried on ball-of-chalking along.