Assuming you have checked them thoroughly for pests on the underside of the leaves congregating around the veins? You haven't fed them a bunch of fertilizer have you?

Dave

Basil Diseases and Pests

No fertilizer added. They did go through a cold spell a week of night temps between 40-45 degrees and a few cold rains bouts during that week. Would you think weather related or bacterial?

Look at Pseudomonas cichorii, bacterial blight, for the black marks.

I think floral nailed it and those weather conditions would be perfect for it.

http://negreenhouseupdate.info/photos/basil-pseudomonas

Dave

Thank you both. Looks like that's what it is.