This small, family-owned Chicago Mexican restaurant specializes in barbecued goat. It is the best barbecued goat I have had, the best accompanying sauce I have had outside of Mexico (you must order it separately), and the best tortillas I have had outside of Mexico. It is one of the best restaurants in Chicago, for my taste perhaps the best.
Here is a short video about the restaurant.
Note also that goats are not in general raised on factory farms. It is a significant question how steeply the marginal cost curve would climb, were we to substitute a lot of goat consumption for say pig or cow consumption. In any case, at the margin it seems like a no-brainer, especially with the Birrieria to guide you.