The sticky liquid is called honeydew. It most likely is being secreted by scale insects feeding on your palm. Examine the fronds and stems very closely for brownish "bumps". These insects attach themselves to the plant and suck its juices. They are difficult to control because they're protected under a shell. Most insecticides are ineffective on all except the young, crawler stage of the scale. Swabbing adults and crawlers with rubbing alcohol will kill the ones that you can reach. It usually takes several treatments to get scale under control.