Sounds like aphids....
I deal with them every year on my indoor pepper plants.
You can use an insecticidal soap to deal with the aphids. I like to rinse my plants
after I treat them (before the sun hits them again). Repeat applications will be required.

Better than soaps or sprays, however, are Ladybugs...and Ladybug larva in particular.

Josh

Considering you are planting in compost, my guess is you have a problem with fungus gnats. The larvae in the soil will eat your new roots. They can be controlled with drenches of a BT solution which can be made by dissolving Mosquito Dunks in water. Al

Al, these pests are covering and distorting new growth, so I wouldn't think fungus gnats,
which are more of a nuisance (and would present a threat to seedling roots if anything).

AV, click the link to the Hot Pepper Forum - many others are dealing with this issue.
The first pic in the Thread ought to confirm whether you have aphids or not.

Aphids?

Josh

Of course Josh is right, gnats do not eat foliage. The flying gnat is a nuisance, the larvae do the damage to the plant. Al

Josh: I loved that Aphids link! Gives me fond (?!?) memories of my summer battles with the little bastards. My only question is that the original poster said his bugs were "chomping" on new growth. Aphids suck, and don't chew. A photo would help.

I think "chomped" is being used figuratively ;-)
But we do need to wait for the original poster to clarify.

Aphids are a yearly joy for me....

Josh