The concept of a human/chimp hybrid is called a humanzee. No humanzees have ever been recorded despite the fact that sexual intercourse between humans and chimps has been recorded on several occasions. This suggests that male-human/female-chimpanzee is not capable of producing viable offspring, at the very least.
As to why, several reasons will contribute: humans and chimps have a different number of chromosomes, making cross-fertility unlikely (although animals with different chromosome numbers can and do breed so this isn't absolute). Humans and chimps are anisomorphically quite different (i.e. the ratios of limbs are different and so on) so it's quite plausible that the growth patterns are not compatible. I'm not aware of any exhaustive studies into reasons why cross-breeding is impossible but it's also quite plausible that there are changes in the chemistry of fertilisation, etc. that will limit cross-breeding.
I'd note, finally, that there's evidence from the X chromosome that the human line continued to have some level of interbreeding with chimps for some million years after the initial split.