They are spider mites. I use a mix of a little bit of neem oil, some liquid soap, and mostly water in a spray bottle. It works pretty well. Usually spider mites are only a problem indoors because of the lack of humidity so with a spraying of neem oil, soap, and water, it will be okay. Neem oil is non-toxic to pets and humans.
Good luck!
-Alex

Are you sure that is not just normal tomentum for a new Chammy leaf?

Would need to see pics of the leaves as well but it you have webs on it
than as Alex mention you probably have the dreaded white spider mites..
you can spray as Alex suggested or take it outside and really jet spray it
off -starting underneath the leaves...make sure your not spraying toward other plants.

Jim is right about the tomentum, all chamaerops have whitish stuff on their newer fronds. You don't see it as much outdoors since the rain and wind take a lot of it off, but it's completely normal. If you have webs then you have spider mites, but don't worry because not all of that white is spider mites, some if it is naturally occuring from the palm.
-Alex