It's not possible to make a definitive diagnosis from an image, but looking around for what this could me came up with a new one for me. Although there are many other identifying elements, one aspect of downy mildew affecting basil (sometimes called basil blight) is the kind of spotting in your picture. Here are two resources with more detailed information that could help you identify if what you're seeing fits all the characteristics: http://extension.psu.edu/plants/gardening/news/2014/basil-downy-mildew and http://vegetablemdonline.ppath.cornell.edu/NewsArticles/BasilDowny.html