This plant is not a palm! It is a Dracaena or Dragon Tree.
There are many different varieties. It is a houseplant here and can easily be cut back. We cut ours back to about 10 or 12" and dripped wax on the ends to stop the milky discharge(our book said to do this). Be sure to wash your hands and not get it in your mouth. In a couple of weeks new sprouts will be coming out the sides of your stalks and you have a short plant again. You can also plant the tops and get new plants from them too! Look it up in any houseplant book or google it to get better propagation instructions. Good Luck.
Below is info I got from googling. I've had afew of these plants over the years and I like to cut them back so that they do bud and form other shoots off of the stem, which it looks like you could very well do that and reduce the height of your plant so that you could keep the original plant in hour home if that's what you want to do.
Just a thought -- on one of your son and wife's anniversaries you could give them back the cuttings off the top of the plant. Usually when I cut mine I just put it aside for a couple of days to let the wound heal over and then I apply rooting hormone to it before potting. If you're a plant lover like I am a lot of my plants have sentimental value and this would keep the thought alive -- love endures!
"Draceana's come from the Dragon Tree, dracaena draco, which is a native plant to the Canary Islands, so their growing habits, likes and dislikes, and temperamental preferences are all very similar.
They can grow to more than 4m (12-13ft) but can easily be kept smaller by pruning the stems prior to spring.
The stems of a draceana marginata are commonly flexible and thin and seem adequately disproportionate to its height and also the foliage that tops it.
If your dracaena is only single-stemmed and you want it to branch out, cut the foliage from the top and reduce the stem to the desired height. Within a few months the foliage will begin to bud from the wound and new branches will grow.
How to propagate dracaena maginata
Draceana's can be propagated by a variety of ways but the most easiest is by taking a cutting from the stem and after applying some rooting hormone to the base (don't forget which end is 'up') firmly push it into some potting mix. Water frequently and apply a liquid fertilizer when the foliage begins to appear.
Other methods of propagating dracaena include air-layering and basal root cuttings.
Fertilising dracaena marginata
Soluble liquid fertilisers are the best form of nutrient release for dracaena's but during their dormant period you can also add some slow release pellets to their growing area or container."
Wow! Beautiful, wish I lived closer I'd take it off your hands. LOL. How about a hospital lobby? I would be afraid to cut it now.
Join freecycle (if their is a group in your area) or try craigslist. It would be a shame if such a nice plant did not find a new home. Good luck.