Oops, sorry, that should be "the parallel evolution of bitter taste"...
Stephen Wooding and colleagues (2006) show that the ability to taste PTC -- long known to be a shared polymorphism in humans and chimpanzees -- evolved separately in each of these species:
It was reported over 65 years ago that chimpanzees, like humans, vary in taste sensitivity to the bitter compound phenylthiocarbamide (PTC). This was suggested to be the result of a shared balanced polymorphism, defining the first, and now classic, example of the effects of balancing selection in great apes. In humans, variable PTC sensitivity is largely controlled by the segregation of two common alleles at the TAS2R38 locus, which encode receptor variants with different ligand affinities. Here we show that PTC taste sensitivity in chimpanzees is also controlled by two common alleles of TAS2R38; however, neither of these alleles is shared with humans. Instead, a mutation of the initiation codon results in the use of an alternative downstream start codon and production of a truncated receptor variant that fails to respond to PTC in vitro. Association testing of PTC sensitivity in a cohort of captive chimpanzees confirmed that chimpanzee TAS2R38 genotype accurately predicts taster status in vivo. Therefore, although Fisher [yes, the Fisher] et al.'s observations were accurate, their explanation was wrong. Humans and chimpanzees share variable taste sensitivity to bitter compounds mediated by PTC receptor variants, but the molecular basis of this variation has arisen twice, independently, in the two species.
Wooding S and 9 others. 2006. Independent evolution of bitter-taste sensitivity in humans and chimpanzees. Nature 440:930-934. DOI link