One major background in direct searches for weakly interacting massive particles (WIMPs) comes from the deposition of radon progeny on detector surfaces. The most dangerous surface background is the 206Pb recoils produced by 210Po decays. In this letter, we report the first characterization of this background in liquid argon. The scintillation signal of low energy Pb recoils is measured to be highly quenched in argon, and we estimate that the 103keV 206Pb recoil background will produce a signal equal to that of a ~5keV (30keV) electron recoil (40Ar recoil). In addition, we demonstrate that this dangerous 210Po surface background can be suppressed by a factor of ~100 or higher using pulse shape discrimination methods, which can make argon dark matter detectors near background-free and enhance their potential for discovery of medium- and high-mass WIMPs. We also discuss the impact on other low background experiments.