Stuck seed casing
This is a pretty common problem - the seed casing isn't pushed off by the growing starter leaves and remains stuck. If left the chilli will often recover or burst it off later, but I've had a few that just die. You can, very carefully, pull it off:
Grasp the chilli seedling with finger and thumb gently. With other finger and thumb grip the seed casing and gently pull, slowly. The casing should slide off with just a little resistance. If it won't budge, don't force it, but leave it another day or two and try again.
