The charging state of aerosols in an 8 m(3) reaction chamber was measured using an electrostatic classifier with a condensation particle counter at different levels of ionization in the chamber. By replacing the Kr-85 neutralizer in the classifier with a radioactively neutral dummy we were able to measure only the aerosols that were charged inside our reaction chamber. These measurements were then compared with measurements using the neutralizer to get the charging state of the aerosols, which refers to the charged fraction of the aerosols compared to an equilibrium charge distribution. Charging states were measured for both positively and negatively charged aerosols while the ionization in the chamber was varied using external gamma sources. We find that the negatively charged aerosols were overcharged (relative to the equilibrium) by up to about a factor of 10 below 10 nm and at 16 +/- 2% from 10 to 70 nm. At higher levels of radiation on the chamber the smaller aerosols were less overcharged while the large aerosols were more overcharged (23 +/- 2%). For the positively charged aerosols only the smallest aerosols were overcharged while those over 10 nm were undercharged (relative to the equilibrium) by 21 +/- 3%. Increasing the radiation on the chamber increased the undercharge above 10 nm to 25 +/- 2% while the overcharge below 10 nm disappeared. The split between positive and negative charges above 10 nm can be explained by differences in mobility of small negative and positive ions. The overcharge below 10 nm can be explained by ions participating in the formation of aerosols of both signs, while the reduction in this overcharge at higher levels of ionization may be explained by faster recombination.