Gleb is not quite right - crossing of various species within the same genus is possible (mules, ligers, camels). Such offspring usually do not reproduce. Interbreeding is practically impossible.
Human and chimpanzee (closest relative) belong to different SPECIES.
Under natural conditions, this is impossible, since representatives of two different species have a different set of chromosomes. Perhaps scientists have already come up with something, but I don't know about it.
I'm a hypochondriac.