The chain should run under the chin for showmanship. First, it looks more professional. Second, the chain is used to cue your horse and that's done more easily with the chain under the chin.
Also, a chain with larger links would be preferred. The smaller links look cheap and are an indicator that the exhibitor may not have much experience or knowledge.
Make sure that the halter is fitted and adjusted to your horse's face. The halter shouldn't gap anywhere. I can take some pictures to demonstrate fitting a halter if that would help you.