Backslang for hat (with /tʃ/ substituted for the /h/).
Meanings
(obsolete, qualifier:costermongers) A hat.
I have a rorty gal, also a knowing pal, / And merrily together we jog on, / I doesn't care a flatch, as long as I've a tach, / Some pannum for my chest, and a tog on. c. 1864, Alfred Peck Stevens, “The Chickaleary Cove”, in Farmer, John Stephen, editor, Musa Pedestris, published 1896, page 161: