Can I eat Chia leaves?
Wikipedia says chia is a plant that belongs to the mint family. According to the wiki article the FDA generally recognizes mint as safe 


  §182.10 Spices and other natural seasonings and flavorings, including
  mint, are generally regarded as safe (GRAS) for food uses in the
  United States.


but 


the wiki article also enumerates two mint species in particular and I don't know why (Peppermint Mentha piperita L. and Spearmint Mentha spicata L.).
I just can't access the original website to check the original terms due to a server error.


Edit: The server works now. Only Peppermint (Mentha piperita L.) and Spearmint (Mentha spicata L.) are generally recognized as safe by the FDA (§182.10). The word "mint" in the cited paragraph from the wiki article doesn't mean the Mentha family but only the plants that are commonly called "mint". I have the impression that in the chia article this mint (Lamiaceae, a family) was mixed up with this mint (Mentha, a genus). As @rackandboneman pointed out, chia (Salvia hispanica) belongs to the family Lamiaceae (common name: mint) and belongs to the genus Salvia (common name: sage).

Edit 2: Sprouts are probably edible. The link directs to an online shop which sells chia seeds with growing instructions. 

I leave this answer for the sake of completeness even it doesn't really answers the question.