YUCK! they look like moth eggs to me. Destroy them before they hatch into palm leaf eating machines.

How do I get rid of them? Do I scratch them off? Do I use a chemical? What should I do?

if its not that big of an infestation than just wiping them off with a wet soapy rag would suffice.

Well, because it was only on 2 leaves and even so, the infestation was on the tip of both, I just cut the tips of those 2 leaves. Would that hurt the palm enough to kill it, or will it be okay? Was it enough to get rid of the infestation, or will it come back?