Cheryl: Can you give a bit more information about the palm? Did you purchase it as a houseplant or could seeds have been dispersed by a squirrel from a neighborhood tree? The squirrels here are always burying seeds from the Pindo Palms into my potted houseplants that are out on the back deck! I'm not good at identifying plants but someone might recognize your palm if you could post more pictures; one of the leaves and one of the trunk/base.
The fruit reminds me of the Lady Palm, Rhapis excelsa:
http://itp.lucidcentral.org/id... but unripe palm fruit can look alike too.
