Ordered mesoporous carbide-derived carbon (OM-CDC) with a specific surface area as high as 2900 m² g^-1 was used as a model system in a supercapacitor setup based on an ionic liquid (IL; 1-ethyl-3-methylimidazolium tetrafluoroborate) electrolyte. Our study systematically investigates the effect of surface functional groups on IL-based carbon supercapacitors. Oxygen and chlorine functionalization was achieved by air oxidation and chlorine treatment, respectively, to introduce well-defined levels of polarity. The latter was analyzed by means of water physisorption isotherms at 298 K, and the functionalization level was quantified with X-ray photoelectron spectroscopy. While oxygen functionalization leads to a decreased capacitance at higher power densities, surface chlorination significantly improves the rate capability. A high specific capacitance of up to 203 F g^-1 was observed for a chlorinated OM-CDC sample with a drastically increased rate capability in a voltage range of ±3.4 V.