If it's from a monster, probably once. If it's from a shop, you can't enchant it.
To check whether (and how often) you can enchant an item, hold down your Ctrl key, click on the item, and then select "Show Item Information". At the very bottom, it'll say "Enchantments", and for every enchantment you can do, it'll either say what you enchanted the item with, or "<Empty>" . Look at the screenshot below for an example. ;P
If the "Enchantment" section is missing, then the item can't be enchanted.
