Green’s Dictionary of Slang

(US) an argument.

1905		F. Hutchison Philosophy of Johnny the Gent 57: ‘We’ll tell him that you’ll get in a chewin' match wit’ him 'bout yer scrappin’ ability’.
1906		C. M’Govern Sarjint Larry an’ Frinds 67: Don’t want to go to bed yet? Wan to have a chewing-match wit’ me ’bout music, do ye?
1950		WELS.
1960		in VT Hist.
1965–70		in DARE.
2001		M. Walsh ‘Chewing the Rag’ at Virtual Vermont 🌐 A chewing match (an argument).