A computational study of capacitively coupled atmospheric-pressure glow discharges in high-purity helium is presented, and the role of trace impurities in such noble gas plasmas is established. Trace impurities result in generation of significant amounts of charged species through Penning ionization and charge exchange reactions. The altered charged species balance in the plasma causes a large change in the discharge impedance when compared to a completely pure noble gas discharge. Peak electron temperatures of the order of 50 000 K and electron densities of order 1011 cm−3 are predicted. Significant electron generation is observed inside the sheath region due to the highly collisional nature of the plasma. This study underscores the importance of modeling the effect of even trace amounts of impurities in noble gas atmospheric-pressure glow discharges.