Chimpanzees may not naturally get HIV, and if given it do not usually go on to develop AIDS, but they can naturally get a strain of SIV (SIVcpz) that causes AIDS and results in a 10-16 fold increase mortality in wild chimps, which is intermediate between that seen with HIV-1 in humans and that seen for HIV-2 in humans.

This is interesting because phylogenetic analysis indicates that SIVcpz is the direct ancestor of HIV-1, which probably arose when a strain of SIVcpz jumped species into humans about 100 years ago. SIVcpz itself was probably acquired by chimps from the monkeys they eat about 500 years ago.

See: Keele B.F et al. Nature Vol 460, 23 July 2009, doi:10.1038/nature08200

Chimpanzees certainly get Hepatitis B, which again occurs naturally in chimpanzee populations
See: Hu X. et al. Proc Natl Acad Sci U S A. 2000 February 15; 97(4): 1661–1664.
http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=10677515

Finally while chimpanzees are resistant to the malaria parasite Plasmodium falciparum they do suffer in the wild from infection by the closely related malaria parasite Plasmodium reichenowi.
Martin M.J. et al. Proc Natl Acad Sci U S A. Vol. 6;102(36):12819-12824 (2005)

There’s actually a lot of interest in the scientific community in looking at differences in susceptibility to different infectious diseases between closely related species, and between sub-species, as this may provide important clues as to how to develop more effective treatments or prevention strategies.

What do you mean the surrounding factors weren’t there – HIV can come about by tainted blood or having sex – how you got it is largely irrelevant in finding a treatment.