Despite retaining a healthy level of skepticism, I post these findings because I am sure they merit some serious attention:
Humans are mainly right-handed for many actions including gestures. This bias is strongly linked to a left cerebral hemispheric dominance for language functions. Whether similar lateralized systems for communicative behaviors are present in other animals is unclear. Here we report the first evidence of strong population-level right-handedness in 60 captive baboons for a species-specific communicative manual gesture. Our findings support the view that lateralization for language may have evolved from a gestural system of communication controlled by the left hemisphere.
Adrien Meguerditchian and Jacques Vauclair, "Baboons communicate with their right hand," Behavioural Brain Research 171 (2006) 170–174.