A gardener working at the house says the tree trimmer was cutting a bunch of fronds when the palm's crown fell on him.
Gardener Jose Martinez says the trimmer shouted as he fell but then went silent.
Firefighters determined the man was dead and covered him with a sheet as they worked to cut him free from a chain that tethered him to the tree.
It took firefighters using a ladder truck about two hours to lower him to the ground.
He was identified as Artmenio Hernandez of Los Angeles.