We report on a one-pot, highly selective chemistry to remove residual catalysts from single-walled carbon nanotubes (SWNTs). The impurities, initially present at similar to 35 wt % and mostly as carbon-coated iron nanoparticles, can be driven below 5 wt % with nearly no loss of SWNTs. The carbon-coated iron impurities are dissolved simply by reacting with an aqueous mixture of H2O2 and HCl at 40-70 degrees C for 4-8 h. This purification combines two known reactions involving H2O2 and HCl, respectively; however, by combining these two typically inefficient reactions into a one-pot reaction, the new process is surprisingly selective toward the removal of the metal impurities. This high selectivity derives from the proximity effect of the iron-catalyzed Fenton chemistry. At pH similar to 1-3, iron is dissolved upon exposure, avoiding the otherwise aggressive iron-catalyzed digestion of SWNTs by H2O2. This extremely simple and selective chemistry offers a "green" and scalable process to purify carbon nanotube materials.