Parliament/Funkadelic (two different bands, same basic people) is
the funk band you need to know, as far as I'm concerned. George Clinton, Bernie Worrel, Bootsie Collins and Eddie Hazel were all masters of their craft. You should also (obviously) check out James Brown - he may be known as the godfather of soul, but a lot of what he did was really funky too. Then there's Tower of Power, who are probably worth a look. And that's pretty much where my knowledge of old funk ends...
Oh, except http://www.youtube.com/watch?v=qe1ScoePqVA

If you like the Chilis and Primus you should also be listening to Faith No More, Mr. Bungle and maybe Extreme too (they're more than
More than Words).