A couple of studies imply that chimpanzees may mourn their dead. I believe they do. I believe that great apes do have that capacity. I've read of the mountain gorillas in Virunga grieving over the loss of a silverback. Heck, even my cats visibly missed old Charlotte who died last August.
If you jump to the comments at the bottom, people took issue with the implication at the end of the article that Jane Goodall would somehow question this grieving behavior. This is because they quote some guy from the USC Jane Goodall Research Center who throws doubt on the premise. Commenters state that Jane Goodall herself witnessed mourning with the Gombe chimps.
I'm sure many will dismiss these studies regardless. It makes it even harder to subject chimps to experiments if you keep discovering these human similarities.