I hope someone can answer this question for me.

Hi - I googled it and found this (see Propagation) http://davesgarden.com/guides/pf/go/1479/#b

I have a tiny Parlor Palm too, so if you try it and it works please let me know. :-)

Ahhh thanks bayareacalifornia! I did a cutting the day I posted my question. Actually it broke off and I removed some leaves, stuck the stem in some rooting hormone and simply stuck it in the potting medium in the pot with the mother plant. I did it on the spur of the moment when it broke off. :-) So far it is still alive. But I have no idea if it is actually rooting or not. If you want, I will keep you updated if you are interested.

Any update, Linda?