Green’s Dictionary of Slang

chest adj.

of a person, puffed-up, self-satisfied.

[US]D. Runyon ‘The Defence of Strikerville’ in From First To Last (1954) 12: There’s a plug sitting behind the desk, looking as chest as a travelling man.
[US]K. McGaffey Sorrows of a Show Girl Ch. xi: She put on such a front and chest that she wouldn’t speak to any of the other girls.

In phrases

get chest (v.) (also go chest)

(US black) to look for a fight; to fight.

[US]H.E. Roberts Third Ear n.p.: get chest v. to look for a fight.
[US]K. Scott Monster (1994) 156: Our dayroom time was mostly spent going chest: Charlie row against Able row.
I’m chest not breast

(US black/teen) a statement of one’s masculinity used to deny suggestions that one is weak/effeminate.

[US]P. Crump Burn, Killer, Burn! 163: Nobody’s going to call me a queer [...] I’m chest not breast.