It looks like the beginning of bacterial leaf spot to me. You could have gotten a contaminated seed. Did you save it yourself or get it from a friend? If you bought a BLS-resistant hybrid, I could be wrong. But otherwise, if I were you, I would cull it as soon as possible. You're just growing more bacterial spores that will make it harder on your future seedlings. Also soak your hydroton in peroxide and wipe down the area around the plant with peroxide as well. Drugstore peroxide is fine; dilute it about 50/50 with water and it won't irritate your skin.

Like I said, I could be wrong about the BLS, but you're so early in the plant's life that you don't lose very much by starting over.

Here is a link that might be useful: BLS resistant varieties

I bet you're using a fluorescent light?

The UV light that isn't converted to visible light by interacting with the phosphor coating of the bulb will actually cause the pepper leaves to produce anthocyanins, which turns the leaves purple.

I have been running into this issue lately myself. Try moving your lights further away if you're indeed using the fluoros.

Anthocyanins can also be produced in excess by pepper plants due to types of stress like too much heat, excess fertilizer, etc.

This is one possibility.