Green’s Dictionary of Slang

haim n.

also hame, haym
[ety. unknown; orig. jazz use hame, a job other than in the music business; ? ref. to collar and hames under collar n.]

[1940s+] (US black) a job, usu. tedious or unpleasant.

In phrases

cop a haim (v.)

[1950s-60s] (US black) to get a job.