Green’s Dictionary of Slang

chalk farm n.3

also chalk
[rhy. sl.; ult. Chalk Farm, London NW1]

1. an arm; thus of direction, ‘hand side’.

[UK]‘Ducange Anglicus’ Vulgar Tongue.
[UK]A. Mayhew Paved with Gold 70: ‘Stand back! [...] and leave the kid alone, or I’ll put out my Chalk Farm (my arm) and give you a rap with my Oliver Twist (fist) over your I suppose (nose) that’ll flatten your chevy chase (face) for you!’ he added, menacingly, between his teeth, as he shook his clenched hand in the air.
[UK]Hotten Sl. Dict.
[US]Trumble Sl. Dict. (1890).
[UK]Mirror of Life 27 July 14/2: But what a change came o'er the scene; / His Chalk Farm outward shot, And Long Ned's bushel caught the blow, / And caught it rather hot.
[Aus]Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 140: ‘Screw the umpcha [sic] on the left chalk,’ look at the chump on your left hand.
[UK]N&Q 12 Ser. IX 345: Chalk-Farm. One’s arm.
[UK]‘P.P.’ Rhy. Sl.
[UK]M. Harrison Reported Safe Arrival 30: Ole Blanco ’adn’t got muck-all on his chalk-farms.
[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]S.T. Kendall Up the Frog 20: On ’is Chalk Farm is a Cousin Ella. ‘In case it starts to France an’ Spain,’ ’e sez.
[UK]D. Powis Signs of Crime 177: Chalk (Farm) Arm (London district).
[UK]P. Wright Cockney Dialect and Sl. 105: Chalk Farm ‘arm’.
[UK]M. Coles Bible in Cockney 37: When they met, Joseph threw ’is chalks around his dad.

2. harm.

[UK]J. Franklyn Dict. of Rhy. Sl.