Just a guess, but it looks like sunscald. This can happen if there is water on the leaves whent he sun is in full force.

Leafminers. The pests are actually inside the leaf. If you look closely at the end of one of the tunnels you may be able to spot the larva. Pick off the affected leaves and cover the plants with lightweight row cover or tulle to prevent the adults from laying more eggs on the plants.

Rodney

Leafminers seconded.

You're right about the leaf miners. There were eggs on the underside of almost every leaf. I ditched the whole thing. I don't care as much about the chard as I do my tomatoes or cucumbers or whatever is next on their menu.

What you had were spinach leafminers. They affect plants like spinach, chard, beets, and other crops and weeds in the spinach family. If you don't have any of these crops growing then you're fine. Also, the adults are a fly. Which means if they were going to affect your other plants they would have already. If you really want chard then like I said before, use row covers or tulle to protect them.

Rodney