To further clarify:
If you go to the back of the rulebook, and check the index for "Upkeep" you'll see this:
Upkeep +X
This object’s controller pays X mana during each Upkeep Phase or this
object is destroyed.
The key word in this description is "Object."
Looking up the word "Object" you'll see this:
Object
Enchantments, equipment, creatures, and conjurations are spells which
become objects in the game, remaining in play after they are cast. The
Mage is also considered an object. Incantation and attack spells do not
become objects.
So, "Objects" can have an upkeep cost. Your enchantment is an Object. The creature to which it is attached is also an Object, but unless your enchantment, by its text, confers an upkeep cost to the creature, it is the enchantment that has the upkeep cost.
So, yeah, everything that's already been said, but with more layout for clarity's sake....and perhaps I'm the only one who wanted that, but there it is, and I'm sleepy, so I'm going to take a nap, now.
...
/end ramble
-nihil