Hi Caity, thanks for using Ask Extension.

This looks like a classic case of Cercospora Leaf Spot is a fungal disease cause the fungus Cercospora beticola. The red/purple spots with gray centers are a sure sign. Spinach and beets also can be infected. This is a common disease that is spread mostly by water splash and wind. It can spread quickly. Warm, humid conditions are the ideal for spore production. Cercospora survives in soil and old leaves, then spreads by water splash, wind, insects, tools, and sometimes seed. Keeping leaves dry and removing infected debris are the biggest controls. Keep the leaves dry, pick off the spotted ones, mulch the soil, give the plants some breathing room, and move your chard to a new spot each year. Good sanitation and fall cleanup will help. A preventative copper fungicide or potassium bicarbonate is beneficial.  Check out the following links.

Cercospora Leaf Spot of Swiss Chard, Beets, and Spinach : Vegetable : Center for Agriculture, Food, and the Environment (CAFE) at UMass Amherst

What's wrong with my plant? : Garden : University of Minnesota Extension

I hope this is helpful.