I would say Yes
The wording in the Rules Compendium (pg 100) is a little different than that of the Player's Handbook:
"The power can be used against a target that is within the specified number of squares of the power's origin square. For example, a melee power that has a range of 1 can normally be used only against an adjacent target, whereas a melee power that has a range of 0 can be used only against a target sharing the attacker's space"
The addition of the preceding and following lines seems to me to imply that the range is a maximum, not a minimum. Supporting this is the actual entry on Melee Basic Attacks (pg 239), which does not specify a range, only that it is a Melee Weapon attack. The entry on Melee weapon (pg 100) says:
"The power can be used against a target within the reach of the melee weapon that is used with the power"
Additionally, it seems a little surreal to suggest that a character is physically unable to hit himself with his own weapon. In terms of the specific power, it strikes me as being akin to Pokemon - The Wild Kobold is Confused - It attacked itself in it's Confusion.
EDIT: Following extended discussion with Wax Eagle, I became curious enough to have a general poke around the net - universally the answers have been in favour of allowing someone to hit themselves if the power didn't specify 'enemy' or 'ally' - though there is disagreement regarding triggering of marks and whether attack bonuses apply (i.e. Hypnotism grants +4).
The reasoning seems to be:
The power lets you hit a creature within range.
A creature in your square is in range.
You are a creature in your square.
Therefore you can hit yourself.
It turns out there is actually rules-support for this last point - the Bard power Mocking Epigram.[DDI]
While affected by the mocking epigram, the target is weakened, and
whenever it hits an ally with an attack, that attack also hits one
enemy of your choice within range of that attack, including the target