Pour epsom salts on the tree stump and along the base. Cover it by securing a tarp around the stump. The salt along with the lack of light will kill the stump. Don't spread salt to other areas of the landscape; salt will kill the other plants and trees.
Drill several holes into the stump. Fill the holes with fertilizer. Fertilizer feeds fungus and will cause wood decomposition. Using the stump as the location of a compost pile is another way to feed the fungus and decompose the wood and roots.
Mix one part of sodium hydroxide with two parts of water in a bucket. Pour the solution over the stump. Repeat this four times over the course of a week to kill the palm stump. Sodium hydroxide is also called caustic soda.
Drill several holes into the stump. Fill the holes with copper sulfate. Cover with a tarp and let it work for one month. Copper sulfate is hazardous material and should be used only where children and animals will not accidentally get exposure. Water the area thoroughly after the stump is dead to dilute any remaining copper sulfate.