At some point there was a common ancestor of both species. Its offsprings diverged into two species that continued evolving into the current humans and chimpanzees.
I don't know anything about the phylogenetic tree of humans and our cousins, but I assume that at some point there was a spectrum (e.g., Neanderthals), but at some point the others got wiped out, without humans splitting any further. Perhaps this is due to the global mobility of humans? What do biologists think?
The reason speciation arises is complex, but its often due to different subgroups of a species exploiting different niches, and thus experiencing differing fitness pulls that eventually give rise to new species.
There are no "intermediate" species because they fit more poorly into either niche occupied by the two other species, and thus are out competed or dont arise in the first place.