What is the history of the RACI chart?
First, RACI is only variant of an entire animal of similar things. Its an example of a Responsibility Assignment Matrix. Gale's "New acronyms, initialisms, and abbreviations" from 1977 lists "RAM -- Responsibility Assignment Matrix [NASA]". So maybe it came from NASA?
A 1972 book called "EDP management controls" by M.D. Wadsworth also lists RAM.