You do. It still happens at interrupt timing, though; if you drop them they don't get to finish their attack.
Assuming the text is exaclty what you list above, there is an issue, though:
When they make the charge, they are presumably at least 2 squares away from you. A reasonable interpretation would imply that you can wait for them to become adjacent and then attack them, but that's only an interpretation; a strict interpretation would imply that you could only make the attack if they were in range of one of your basic attacks (a ranged basic, perhaps) when they began the charge.
Certainly, you can "repel" a charge with a ranged basic (assuming there isn't missing text that implies it has to be a melee basic), and if you do so, you can do it when the enemy begins the charge, not once they're adjacent (really useful if they enemy is using a readied action and is therefore capable of making opportunity actions of their own). But the intent would seem to be that you can also make a melee basic, yet without reach you can only do so with a very generous GM ruling.