This expression comes from the Jamaican Creole and has spread throughout the Caribbean, and from there to France especially through immigration and the Raga-Dancehall music scene, known for its violent, macho and tremendously homophobic lyrics, where it is easy to find songs in which it is encouraged to kill or attack the Chichi-man.
In its origin the expression Chichi in Creole makes reference to termites, and although in Internet the usual explanation relates to the fact that termites and gays are considered a plague, it seems nevertheless, that the use of Chichi-man and the relationship with termites has to do with orality, perhaps because of the big mouth, due to the sound or because of the insatiable appetite of the termites “who eat it all”.
We can then distinguish the Chichi-man, the one who practices oral sex, from the batty-man or batty boy, coming from the English term butt, and reserved for those who practice anal sex.
In both cases it seems that these expressions in origin did not refer specifically to sexual orientation, but simply to the concrete sexual practice regardless of whether the actor was homo or hetero, although over time they became the more offensive expressions with which gays are named in Jamaica.
Related: to belonging to Jamaican Creole: Batty Bwoy, Batty-man, Booga-man, Chichicam, Fish, Funny-man, Poonga-man, Beeps, Beeps-man, Macoume.