Recently, the first drug in a new class of antiretroviral HIV drugs was approved, the fusion inhibitor enfuvirtide. We develop a mathematical model that describes the binding of the virus to T cells. We model the effect of enfuvirtide upon this process using impulsive differential equations. We find equilibria and determine stability in the case of no therapy and then when therapy is taken with perfect adherence. We determine analytical thresholds for the dosage and dosing intervals to ensure the disease-free equilibrium remains stable. We also explore the effects of partial adherence. Our theoretical results suggest that partial adherence may, at times, be worse than no therapy at all, but at other times may in fact as good as perfect adherence. It follows that patients should be counselled on the importance of adherence to this new antiretroviral drug.