@Lisa Shock I can confirm it is Chinese. The larger script is an old, now obsolete Chinese script, most of which I can't read. (This is no guarantee of age, though.) The smaller writing is more modern Chinese, but not very clear. The only bit I can make out is 竹林七贤 in the second picture. This refers to The Seven Sages of the Bamboo Grove (240--249AD ), as does the image. I'm guessing the old writing is part of one of their poems.
I would agree it is probably some sort of vase or perhaps a calligraphy brush holder.
I will ask friends who know more about these things (and have better eyesight than me) and let you know if they come up with anything.
Can you give me its dimensions, please?